Atletico Madrid striker Diego Forlan scored against Liverpool for the second time in a week to end the Merseysiders' dreams of a third European final in five years.
The former Manchester United forward, who hit the only goal in the first leg, stabbed home the crucial extra-time away goal which booked their place in May's Europa League final despite a 2-1 defeat at Anfield.
Alberto Aquilani's 44th-minute strike had ensured the game went into the additional 30 minutes and despite Yossi Benayoun putting his side ahead, Forlan - much derided during his time in English football - had the last word.
Twice previously in this competition Liverpool had come back from first-leg deficits - against Lille and Benfica - but on this occasion even a win was not enough.
How they missed injured striker Fernando Torres, watching his former club take on his current employers from the stands, after dominating most of the game but failing to finish off their opponents in normal time.
But it was not the lack of goals which did for them in the end, but the one they let in at the Kop end to a familiar foe.
Liverpool had needed an early boost and they almost got it after just nine seconds.
Daniel Agger's long ball picked out Benayoun in the penalty area and his low shot from a narrow angle was turned behind by goalkeeper David de Gea, who had an easier save when Aquilani shot straight at him in the 11th minute.
It was a sign of things to come as Atletico's gameplan of sitting back and counter-attacking was restricted to just the former.
But the Spanish side, driven by the knowledge an away goal would strengthen their position considerably, still posed an occasional threat and Jose Reina dived low to his right to turn Raul Garcia's long-range effort around the post midway through the half.
Still Liverpool pushed forward and Dirk Kuyt, who recovered from a calf injury to lead the line, was only inches over as he slid into the six-yard area to deflect Javier Mascherano's cross.
The game was becoming more open but when Sergio Aguero went round Reina from Jose Antonio Reyes' perfect through-ball he opted to cross rather than shoot from a narrow angle and Forlan could not make up the ground.
Liverpool thought they had scored the goal they desperately wanted when Steven Gerrard curled in a 32nd-minute free-kick and Agger headed into the bottom corner only to be flagged offside.
Gerrard was booked for a needless foul on Aguero as the half drew to a close and frustration levels began to rise at Anfield.
But a minute before the interval the breakthrough finally came with the simplest of moves and the most exact of finishes.
Stand-in right-back Mascherano's throw down the wing was picked up by Benayoun whose cross was missed by Kuyt but found Aquilani who curled a low shot just inside De Gea's left-hand post.
With honours even Liverpool's approach play was more patient and measured as the second half began.
But the optimism around Anfield which was tangible before the break had been replaced by a growing sense of anxiety and the players could feel it, with Benayoun shooting well over from 25 yards.
Urged on by the Kop, Liverpool found an extra gear and when left-back Glen Johnson cut in and whipped in a right-footed shot De Gea could only parry it over the crossbar, but the goalkeeper was able to claim Gerrard's corner unchallenged.
The last 10 minutes saw Atletico have probably their best spell of the game but Forlan crucially mis-controlled the last chance of regulation time having sprung the offside trap.
Five minutes into the added period Liverpool went ahead for the first time.
A Gerrard free-kick was only half-cleared and Lucas lobbed the ball over the inside-left channel where Benayoun, played onside by Antonio Lopez, drilled home left-footed with De Gea getting a hand to the shot but failing to keep it out.
Substitute Jose Manuel Jurado's 20-yard effort inches wide of the post was a warning Liverpool failed to heed as in the 102nd minute Atletico scored a the vital away goal when Reyes beat Johnson to cross for the unmarked Forlan to stab home.
The second period was notable only for Simao Sabrosa firing just over as Liverpool's European dreams - and their hopes of a successful conclusion to their season - were extinguished.Reuse content