Newcastle crashed out of the Uefa Cup after Sporting Lisbon overturned a 1-0 deficit from the first leg to win 4-2 on aggregate in a thrilling game.
Kieron Dyer put Newcastle ahead, slotting between Ricardo's legs but Marius Niculae equalised with a powerful header.
After the break, Sa Pinto knocked in the rebound from Pedro Barbosa's shot and Beto headed his side's third.
Fabio Rochemback sealed the victory late on with a cool finish.
Sporting will now meet AZ Alkmaar in the semi-finals after the Dutch side beat Villarreal 3-2 on aggregate after a 1-1 draw at home.
Newcastle will look back on a number of chances missed - although neither side gave a defending masterclass.
The hosts started quickly and put Newcastle under pressure for the opening 20 minutes without creating any clear-cut opportunities.
And when the first one came, it went Newcastle's way and Dyer was ruthless in his execution.
His pace took him clear and he precisely placed the ball between Ricardo's legs to score against the run of play.
Dyer almost scored another goal in the first half but clipped his shot just wide from a similar position.
He later limped off with a hamstring injury just before the hour mark - and his pace and direct approach-play was sorely missed.
Before then, Sporting earned a reward for their all-out attacking approach.
Niculae showed great composure to direct his header beyond Shay Given to level the score on the night.
Newcastle had chances to regain the lead - the best falling to Lee Bowyer - but his shot blazed high and wide.
But the visitors were thankful to keeper Given, who made a tremendous save to keep out Jao Moutinho's thumping volley.
After the interval, Newcastle substitute James Milner shot straight at Ricardo as Sporting wobbled at the back.
And fellow substitute Patrick Kluivert failed to play a decent ball across the penalty area to Shearer as another opportunity went begging.
Then came the Sporting onslaught.
Given did well to parry Barbosa's shot from outside the box but could do nothing to stop Sa Pinto slotting home the rebound.
At that stage, Newcastle would still have gone through on the away goals rule.
But it was a scenario that looked unlikely, given Newcastle's defending - and so it proved.
Pressure told again when Beto headed home from Rochemback's corner to put Sporting in control for the first time.
And any hopes of a Newcastle recovery were dashed when Rochemback punished a mistake by Stephen Carr to slide the ball past Given to seal victory.
Sporting: Ricardo, Anderson Polga, Rogerio, Rui Jorge, Beto, Carlos Martins (Pedro Barbosa 67), Rochemback, Joao Moutinho, Sa Pinto (Custodio 89), Niculae (Pinilla 75), Douala.
Subs Not Used: Nelson, Tello, Miguel Garcia, Mota.
Booked: Beto, Anderson Polga.
Goals: Niculae 40, Sa Pinto 71, Beto 77, Rochemback 90.
Newcastle: Given, Carr, Bramble (Andrew O'Brien 57), Taylor, Babayaro, Jenas (Milner 46), Faye, Bowyer, N'Zogbia, Dyer (Kluivert 60), Shearer.
Subs Not Used: Harper, Ameobi, Ambrose, Butt.
Booked: Bowyer, Taylor.
Goals: Dyer 20.
Ref: Peter Frojdfeldt (Sweden).