Liverpool had progressed eight times after losing the first leg 1-0 in Europe but failed at the ninth attempt, being unable to take advantage of their blistering first half performance.
The tone was set after only 12 seconds as Yossi Benayoun had a shot blocked by the young Madrid keeper David de Gea.
The hostâ€™s continued their aggressive start with three quick corners but inevitably the tempo dropped and Madrid showed how dangerous they could be on the break.
But the Reds got back into the game and Dirk Kuyt scooped over after a flowing move.
Madrid hit back and Sergio Aguero rounded Pepe Reina but chipped the ball ahead of any team-mates.
On the stroke of half-time the pressure finally paid for the home side.
Benayoun cut the ball back and Alberto Aquilani hit the ball first time, low into the corner of goal.
The second half was a more low key affair as Madrid retained possession and Liverpool failed to regain the initiative of the first half.
Glen Johnson went closest in the 80th minute but de Gea palmed over.
The Reds then took the lead on aggregate within four minutes of the start of extra time.
Lucas delicately chipped pass found Benayoun whose first time cross shot nestled instantly in the far corner.
Madrid may have had an average La Liga season but had shown on the night how dangerous they could be, and one goal would see them progress on aggregate.
Liverpoolâ€™s miserable season looked to being redeemed but the visitorâ€™s gave notice when substitute Jose Jurado shaved a post then Reina was fortunate when a long range shot bounced off his chest to safety.
But the inevitable happened on 102 minutes and the goalscorer was a former Manchester United striker.
Johnson hesitated and Jose Reyes took advantage to cross for the unmarked Diego Forlan to smash home from close range.
The Spanish outfit easily played out the rest of extra time as Liverpool simply ran out ideas, rather like their season.
For Madrid they head to the finals in Hamburg and a meeting with Fulham on the 12 May and who would have predicted back in August that Fulham would be the Premier Leagues most successful side in Europe this season.