Two stunning second-half goals by Gylfi Sigurdsson ended Scotland's hopes of reaching the U21 European Championship.
Trailing 2-1 from the first leg of the play-off, Scotland hit the post after 15 minutes through Jamie Murphy.
But it was the impressive Sigurdsson who scored Iceland's opener with a sweet curling finish from 20 yards.
Chris Maguire levelled immediately from the re-start with an amazing strike from the halfway line before Sigurdsson rifled in a second from distance.
Manager Billy Stark had demanded an improved display after the defeat in Iceland on Thursday.
If the first 20 minutes were anything to go by, the Scots had paid heed to Stark's words.
They harried the athletic visitors, who were boasting eight full internationals, attacking them with an enthusiasm that was utterly absent from the senior team's display in Prague on Friday.
In the early action, Liverpool defender Danny Wilson was nudged off the ball as he waited to connect with a dropping ball eight yards out, but a penalty would have been harsh.
Aberdeen striker Maguire and Motherwell's Jamie Murphy looked slick and caused jitters in the Icelandic back line, yet it was not one-way traffic, as three shots reminded the Scots of the danger.
Rurik Gislason whipped one past Alan Martin's right-hand post from 25 yards, then Paul Hanlon managed to deflect an effort by star player Sigurdsson, a £7m signing by Hoffenheim, past the post after a surging run from his own half.
This was followed by a meaty thump by Coventry's Aron Gunnarsson, whose low effort was parried by Martin, probably the best the keeper could have done.
The best chances, however, fell to the Scots. Falkirk left-back Tam Scobbie launched a beautiful long pass from the edge of his box down the inside-left channel which had Murphy scarpering like a greyhound out of the traps.
Showing great balance and technique he jinked past the full-back and hit his shot off the post. The ball rebounded to Barry Bannan, who cracked a left-foot shot which Andres Johannesson dived to head off the line back to the Aston Villa winger, who knocked his overhead kick six inches past the post.
Bannan was teasing the Icelandic defence with his trickery down the left and looked a decent source for the goal that would take Scotland through on away goals.
His move to the opposite flank produced a chance for David Wotherspoon as his swift attack from right midfield and cross into the box found the Hibs midfielder, on home turf, alone at the far post.
Sadly for the home team, his ball across goal was hit too firmly for any team-mate to slide home.
Maguire celebrates his incredible strike from the halfway line
Having witnessed the carnage caused by Bannan on the left wing, Hjortur Valgardsson decided the best way to stop him was to scythe him down, for which he was booked by Swedish referee Markus Strombergsson.
Wilson headed Bannan's resultant free-kick wide.
Iceland were the top scorers in the group stages, with 29 goals in eight games, and in the second period it was as if Scotland realised how fatal conceding a goal would be.
Bannan no longer offered the same threat and the Scots retreated.
In the 54th minute Maguire was presented with a chance on the left-hand side of the box but only a terrific saving challenge by Elfar Freyr Helgason prevented the Scots' number nine from testing Arnar Petursson.
Paul Coutts drove into the box and rifled a rising left-foot shot straight at Petursson, but minutes later Sigurdsson silenced the home crowd when he was given too much space to run at the defence, cut inside from the left and curled a delicious ball round Martin.
The Icelandic goalkeeper ran to the other half to join the celebrations and, incredibly, did not get back into his goal in time for the re-start.
Maguire was alert to Petursson's lapse and pinged a stunning shot over the horrified keeper's head and into the net to make it 3-2 to the visitors on aggregate with 15 minutes remaining.
With the crowd roaring them on, the Scots pushed forward and were caught out with another wonderful goal by Sigurdsson, a rasping right-foot shot into the top corner from 25 yards, which ended the play-off as a meaningful contest.
Stark sent on David Goodwillie for Watford's Stephen McGinn and David Templeton for Jamie Murphy but there was no way back - the Scots' admirable attempts to reach the finals in Denmark had come to nothing.
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