Diego Forlan's 102nd minute goal ended Liverpool's hopes of a first trophy in four years as Rafa Benitez's side were denied a place in the Europa League final by Atletico Madrid on the away goals rule.
Yossi Benayoun's 95th minute goal, which gave the hosts a 2-1 semifinal aggregate advantage, looked to have given Liverpool a place in their third European final in six seasons.
Trailing 1-0 from the first leg, Alberto Aquilani had levelled the aggregate scores with a sublime finish before Benayoun struck early in extra time.
But former Manchester United striker Forlan sent the Spaniards through to face Fulham in the May 12 final in Hamburg and left Liverpool to reflect on a fourth successive season without a trophy.
Fulham bounce back to reach final
London: Fulham came from behind on Thursday to beat Hamburg 2-1. After a goalless draw in the first leg, Mladen Petric's first-half freekick seemed to have put Hamburg in control.
But Simon Davies levelled midway through the second half, before the Hungarian forward Zoltan Gera forced in the winner. “It's the most important goal I have ever scored so I'm very, very happy. It's amazing,” Gera said. “We did so well, every single player.”