Goalflashes and major incidents (all times BST):
2134: Ramos was dancing a jig of delight on the touchline even before the fourth goal went in - now he is walking across the pitch to the Sevilla, head in hands, savouring the moment.
McClaren stood alone waiting for his disconslate players to trudge towards him before finally going to join them in the centre-circle.
He could not bring Boro European glory with his final act before leaving for the England job but he still deserves praise for getting them this far in the first place.
2132: FULL-TIME Middlesbrough 0-4 Sevilla
A hugely disappointing end to a thrilling Uefa Cup run for Boro as Sevilla start to celebrate winning the first major European trophy in their history.
Steve McClaren can only reflect on what might have been as he ends his time as Middlesbrough manager.
2130: GOAL Middlesbrough 0-4 Sevilla
This is becoming a bit harsh on Boro now as Enzo Maresca, going for his hat-trick, has his shot saved by Mark Schwarzer only for Fredi Kanoute to slam it into the back of the net.
2129: With less than five minutes to go the Sevilla fans have begun their celebrations - and they are likely to last a while.
You could say former West Brom midfielder Enzo Maresca's third goal killed Boro off - but they looked as though they had given up once they went 2-0 down.
McClaren has reappeared but his only aim now must be prevent a complete rout, rather than rouse a comeback - Boro have recovered from 3-0 down before this season but they have run out of time and ideas on this occasion.
2126: Steve McClaren allows Lee Cattermole a taste of a European final as he replaces Mark Viduka.
Before play restarts Antonio Puerta replaces Adriano Correia for Sevilla.
2125: GOAL Middlesbrough 0-3 Sevilla
That really is it now as Enzo Maresca drills in his second goal with a low shot from the edge of the area after Jesus Navas' right-wing cross is headed out of the box.
Maresca is booked for removing his shirt in celebration.
2124: A first booking for Boro as Fabio Rochemback is booked for a foul on Fredi Kanoute.
2123: High, wide and horrible is the way to describe Pep Marti's free-kick from 25 yards out which ends up in the crowd.
2121: Sevilla defender Julien Escude collects his side's second yellow card.
2120: Not much attention has been paid to the Sevilla dugout this evening but their second goal brought a mass exodus from everybody in there to join the celebrations - apart from Ramos.
He barely moved and is still stood in his technical area impassively surveying the game - McClaren is nowhere to be seen now - he probably needs a sitdown after all that.
Some Boro fans are leaving the ground - have they not been paying attention during their run to the final?
2119: GOAL Middlesbrough 0-2 Sevilla
It looks all over for Boro now as Sevilla suddenly break out and double their lead.
Jesus Navas advances into the right-hand side of the area and squares for Fredi Kanoute. His shot is blocked by Mark Schwarzer but falls for former West Brom player Enzo Maresca to sweep home.
2119: Boro are being forced back by Sevilla as they pass the ball around just inside the Sevilla half before the only remaining defender Chris Riggott hoists it out of play.
2117: The referee waves away Boro claims for a penalty as Mark Viduka goes down under the challenge of Javi Navarro. Steve McClaren holds the back of his head with his hands in disbelief.
McClaren is waving his troops forward again - but with four strikers already up there, he should really be concentrating on finding a way of feeding them the ball.
Boro's shout for a penalty brings a deafening roar - of desperation perhaps?
- from the Boro fans and everyone on the bench.
McClaren has his hands in his pockets though, only removing them to signal for a long diagonal ball to be played towards Maccarone's head - surely he has more up his sleeve than that.
2116: Another chance goes begging as Jimmy Floyd Hasselbaink finds Mark Viduka 20 yards out but his low shot skids past the far post.
2116: There are just 15 minutes left now for Boro to rescue their European dream.
They have come a long way to end at the final hurdle - and with only one clear cut chance - for Viduka - to show for their efforts so far, it appears McClaren will end his Boro tenure with a whimper rather than a bang.
The Boro fans know time is running out - they are chanting for two more Sevilla goals so they can begin one of their famous comebacks.
2114: The masked Mark Schwarzer has to be alert as he dives to turn away a goalbound shot from full-back Daniel Alves.
2113: Sevilla make their second change with goalscorer Luis Fabiano being replaced by Brazilian compatriot Renato. They switch their formation to leave Fredi Kanoute as the lone striker.
2112: Fredi Kanoute squanders a chance for Sevilla as his shot drifts harmlessly into his side's fans behind the goal.
2111: Boro may be making a different substitution to the one they planned as Franck Queudrue is forced off by injury to allow this season's top scorer Yakubu on.
That makes four Boro strikers on the pitch now, as many as England are taking to the World Cup finals.
2111: Boro have lost the impetus they had immediately after the interval and the Sevilla fans are sensing their team are again taking this game by the scruff of the neck.
McClaren is certainly nervous now, hand to his mouth, and he can't decide whether to bring Yakubu on or not - four times he has had the chance, with the striker stripped and ready and each time he has told the fourth official not to bother.
2110: No, it's not as Jimmy Floyd Hasselbaink's expertly-floated free-kick goes agonisingly just over the bar.
2109: Fabio Rochemback is brought down by David outside the area - is this the moment for the equaliser?
2108: It is set to be all-out attack for Middlesbrough again, as in the previous two rounds, with Yakubu warming up.
2106: Steve McClaren sits down for the first time all match - he has spent most of the game standing at the edge of his technical area. His assistant Steve Harrison is up in the stands making notes.
2106: The ball is bobbing around the Sevilla area once again but George Boateng's shot is blocked by the falling Javi Navarro.
2102: Boro have dominated the opening stages of the second half but Sevilla find time to launch an attack with Jesus Navas speeding down the right but his cross is rapidly cleared by Gareth Southgate.
2100: Massimo Maccarone comes close to making another impact on this competition as he fires the ball in from the right wing and Andres Palop has to push it over his bar.
2058: McClaren is up and about too - taking his notes out of one pocket and immediately putting them in the other.
Maybe that is a secret code to tell his players to pour forward, or possibly just nervous fidgeting, but he has got the message across somehow and Boro are going for it.
2058: Is this the slice of luck Boro need? Stewart Downing hoists the ball into the Sevilla area and Daniel Alves slices his clearance to concede an unnecessary corner.
However once again they fail to take advantage and the ball is cleared.
2055: This is more like it - the Boro fans have something to shout about at last.
They're on their feet too, after warming their seats for most of the first half.
2053: The game's first yellow card goes to defender Daniel Alves for a foul on Stewart Downing on the left wing.
2052: A great chance for Boro to level as Chris Riggott heads on to Mark Viduka eight yards out but his half-volley is well blocked by keeper Andres Palop.
The ball goes straight up the other end and Jesus Navas outpaces Gareth Southgate before firing just wide.
2051: A flowing break from Sevilla almost sees them double their lead. Pep Marti races half the length of the field before feeding Adriano Correia and his curling shot from just outside the area is not too far away from the far post.
2049: Maccarone has pushed forward and David is now having to stay deep to track him.
2047: The second half gets under way.
2046: Steve McClaren acts on Chris Bevan's advice and makes the change with Massimo Maccarone coming on for James Morrison.
Cometh the hour, cometh the man? Maccarone has done it before for Boro remember but the Sevilla defence is being superbly marshalled by Escude and looks a tough nut to crack.
Former Tottenham striker Fredi Kanoute is Sevilla's replacement - with Javier Saviola making way.
HALF-TIME VERDICT by BBC Sport's Chris Bevan in the stadium:
The half-time whistle is a welcome one for Boro. Steve McClaren will have to earn his corn now if they are to turn this one around.
There seems little cohesion in their play and the whole midfield is often being byapssed. Boro don't need a miracle yet but super sub Massimo Maccarone is on the bench again if they do.
However they need their manager to act now to reverse the flow of this game.
2031: HALF-TIME Middlesbrough 0-1 Sevilla
A disappointing first half ends with Boro trailing to Luis Fabiano's goal and needing to up their game to turn things round in the second half.
2030: The Boro fans are trying to encourage their team but they have had little to cheer about so far. Like Hasselbaink they want their players to get forward but they need to get the ball first.
2030: Boro hit back and from a left-wing corner by Stewart Downing, the ball ricochets off James Morrison on the edge of the area and loops over the bar.
2028: Another right-wing free-kick by Pep Marti, this time much closer to the goalline, and Fabio Rochemback needs to put it out for a corner.
From the flag-kick, Mark Viduka miscues as he tries to clear but luckily the ball flies to safety.
2027: Pep Marti floats a right-wing free-kick into the Middlesbrough area but Julien Escude can only plants a header well wide of the near post.
2027: Hasselbaink is at it again - imploring James Morrison to close down Sevilla left-back David, without success. It is a frustrating night so far for the Dutchman, like Viduka he has been reduced to chasing hopeful long-balls and is not being given a sniff by Julien Escude.
2026: George Boateng puts in a crunching tackle on Pep Marti in the centre circle but German referee Herbert Fandel considers that a free-kick is sufficient punishment.
2022: McClaren is on the move again - briefly venturing outside his technical area, and now managing to applaud his players while carrying a hefty stack of notes.
Impressive stuff - now all he needs to do is work out how to get his side going - they are clearly second best so far..
2021: Steve McClaren goes back inside his dugout - maybe to ask his sports psychologist Bill Beswick what his next move should be.
2020: Boro try to build down the left but Fabio Rochemback's ball towards the penalty area fails to find a colleague.
2019: Stewart Downing swings in another corner from the right. It is better than his first but is headed away from the six-yard box by the Sevilla defence.
2017: Jimmy Floyd Hasselbaink shows signs of frustration as Sevilla are again allowed to build from the back. Boro seem to be almost inviting Sevilla on to them and the wingers seem to be instructed not to go past half-way once Sevilla have the ball.
This is allowing the Spaniards to march forwards, much to Hasselbaink's annoyance, and it was this tactic that led to the goal.
2015: The Sevilla fans are still up on their feet after their goal - the whole top section of their end is literally jumping - waving scarves, banners, flags and anything they can get their hands on.
The Boro supporters are understandably more subdued, but then again they have to wait until they are 3-0 down before their team starts playing don't they?
2014: Sevilla have their tails up at the moment and Adriano Correia advances on the Boro area before unleashing a fierce shot from 20 yards which flies just over.
2011: GOAL Middlesbrough 0-1 Sevilla
Disaster for Boro as Luis Fabiano gets in ahead of Chris Riggott to head Daniel Alves' right-wing cross into the far corner of the net and put Sevilla ahead.
2010: Sevilla's attacking ploy of playing the ball short to Saviola with Luis Fabiano spinning off him is bearing fruit (oranges?) so far - but Boro are getting nowhere launching high balls up to Mark Viduka. McClaren needs to use his side's width if they are to break down the Spaniards.
2010: Gareth Southgate tries to get James Morrison away on the right but the pass is overhit and rolls out for a goal-kick.
2006: The Boro fans have been subdued for a while but with Downing seeing more and more of the ball on the left they have rediscovered their earlier volume.
For someone who was not supposed to be able to defend, Alves is doing a good job of keeping the England man quiet though.
2005: The Sevilla fans shout "handball" as Javier Saviola's shot from the edge of the area hits Gareth Southgate's hand inside the area but there was no question of intent and the referee correctly waves play on.
2003: Maybe we spoke too soon. McClaren is on the edge of the technical area now, waving his players forward, if only to get at least one of them in the Sevilla half.
Who said he was too negative to be in charge of the national team?
2001: So far the most animated that the next England manager has got is to take a swig from a bottle of water. No fist-pumping yet but maybe he doesn't want to annoy Sven-Goran Eriksson who is watching in the crowd.
2000: Stewart Downing and a Sevilla defender appear to clash briefly off the ball but the officials do not spot the incident and play continues.
1959: Boro win their first corner of the game but Stewart Downing's flag-kick is easily headed clear by Pep Marti.
1959: Steve McClaren is on his feet at last, leaning on the side of his dugout and shrugging his shoulders as a Boro attack breaks down.
1957: Much was made before the game of Stewart Downing's battle with Daniel Alves on the left, with the Sevilla man supposedly a weak link defensively. He is certainly giving Downing plenty of space on that flank but so far Boro cannot find a way to bring their wideman into the game.
1953: Chris Riggott is the hero for Boro a minute later as he and Mark Schwarzer combine to force Luis Fabiano's effort out for another corner which also comes to nothing.
1952: Danger for Boro as Sevilla's David escapes down the left and Chris Riggott has to slide in to divert his centre out for a corner from inside his own six-yard box.
1951: The noise inside the ground is still deafening with the opposing fans trying their hardest to drown each other out. Boro are singing their hearts out while Sevilla are whistling or cheering, depending on whether they are in possession or not.
No sign of Steve McClaren in his technical area yet but Ramos is up and occasionally strolling around - although mostly standing with his arms crossed looking non-plussed.
1950: Fabio Rochemback takes the set-piece and his fierce goalbound drive has to be pushed away by keeper Andres Palop.
1949: Middlesbrough win a free-kick 25 yards from goal as captain Javi Navarro clumsily climbs all over Mark Viduka.
1947: Sevilla's Brazilian right-back Alves Daniel has the game's first effort with his shot from 20 yards fizzing past the Middlesbrough post.
1945: Sevilla get the game under way.
1944: A mass of photographers capture Steve McClaren making his way into the Boro dugout as he prepares for his last game in charge.
The Sevilla coach Juan de la Cruz Ramos is strangely ignored!
1943: The ground is alive with noise and colour as the players file out on to the pitch accompanied by local schoolchildren, while those puzzling acrobats somersault out of the arena behind them.
1941: The Sevilla fans unveil three huge banners proclaiming "Somos Grandes" while the Boro fans match them by passing a massive 'Boro' flag around their end of the ground.
1937: Hans is the Uefa Cup ambassador!
The ballloons have just been released into the sky to the sound of cannon fire and there are now acrobats tumbling over the pitch - hopefully the players won't be imitating them later.
1935: Former PSV and Nottingham Forest keeper Hans van Breukelen brings the Uefa Cup out on to the pitch and parades it around the ground, as the players prepare to come out.
Hundreds of children follow him carrying orange and white balloons to greet the teams.
1930: With 15 minutes to go until kick-off, the stadium is almost full. Both club's anthems are played to take the atmosphere in the ground to a new level.
Boro's tune is a fist-pumping affair while Sevilla have a more traditional Spanish number - but both have the same effect on their respective supporters.
1920: The stadium is split in a sea of red and white with both sets of players out on the pitch now warming up. Boro keeper Mark Schwarzer is not looking affected by his mask, throwing himself around his area and collecting crosses confidently.
1911: The Middlesbrough team is read out to a raptuous reception, although the Boro end is still not even half full. The fans that are here have just been treated to a re-run of their route to the final - with every goal greeted as though it had just gone in.
1900 BST: Sevilla's fans are making a deafening noise inside the Philips Stadion in Eindhoven as the Middlesbrough contingent steadily make their way into the ground.
Middlesbrough keeper Mark Schwarzer starts in his first game since fracturing his cheekbone while Mark Viduka and Jimmy Floyd Hasselbaink get the nod in attack.
Schwarzer is set to play in a protective mask while Hasselbaink, along with influential captain and centre-back Gareth Southgate, has shaken off a hamstring injury to make the starting XI.
Sevilla have Javier Saviola and Luis Fabiano spearheading their strikeforce with former West Ham and Tottenham forward Fredi Kanoute on the bench.
Middlesbrough: Schwarzer, Parnaby, Riggott, Southgate, Queudrue, Boateng, Morrison, Rochemback, Downing, Viduka, Hasselbaink.
Sevilla: Palop, Daniel, Navarro, Escude, David, Navas, Marti, Maresca, Correia, Fabiano, Saviola.
Referee: H Fandel (Germany)