Diego Forlan struck an extra-time away goal to end Liverpool's Europa League hopes and book Atletico Madrid's place in the final against Fulham on 12 May.
Trailing 1-0 from the first leg in Spain, Liverpool levelled the tie when Alberto Aquilani converted Yossi Benayoun's cross with a fine finish.
And they added a second early in extra time through Benayoun's half-volley.
But former Manchester United striker Forlan fired home a Jose Antonio Reyes cross to confirm Liverpool's exit.
The result will simply add to the gloom surrounding Anfield in what has been a miserable season on and off the pitch.
Rafael Benitez's side suffered early exits in both domestic cup competitions and the Champions League, while they currently languish seventh in the Premier League.
Meanwhile, the club are carrying significant levels of debt, have been riddled by rumours of boardroom unrest and seem unwilling to put an end to constant speculation surrounding the future of Benitez.
In fact, the build-up to this match was somewhat overshadowed by the latest round of speculation linking the 50-year-old with a summer move to Juventus.
Benitez claimed no-one at the club had tried to talk him into staying and expressed frustration that a number of other managers had been linked with his job.
While there was no sign of disunity as the home crowd whipped up a electric pre-match atmosphere, Liverpool may regret failing to capitalise on their early pressure.
Only 10 seconds were on the clock when Dirk Kuyt flicked Daniel Agger's long ball into the path of Benayoun, who saw his low drive saved by the legs of keeper David de Gea.
Atletico looked rattled and it seemed an opening goal was inevitable as Liverpool bombarded them with a flurry of corners, but the visitors held firm and soon asserted their authority on proceedings.
The superb Sergio Aguero returned from suspension to lead their attack and linked particularly well with Reyes, Simao and first-leg goalscorer Forlan.
It was, however, the less heralded Raul Garcia who had their first clear-cut opportunity with a skidding effort from 30 yards that was palmed around the post by the diving Pepe Reina.
Kuyt side-footed Javier Mascherano's cross just over the bar following a delightful passing move, while Aguero was sent clear by Reyes but had nobody to cross to after rounding Reina.
Liverpool, bidding to reach a third European final in six years, thought they had taken the lead but Agger's header was correctly ruled out for offside.
Fortunately for the hosts, nothing would deny them when Benayoun crossed from the right and Aquilani turned a superb first-time finish into the bottom corner shortly before half time.
Atletico settled quickest after the restart - passing, moving and retaining possession with a real swagger - but Liverpool's defence was unmoved.
Simao and Paulo Assuncao put speculative shots off target, and at the other end Antonio Lopez made a vital interception with Benayoun ready to pounce on a Gerrard cross.
De Gea had to react well to tip a fizzing Johnson strike over the bar but Atletico were on top and Gerrard made a crucial clearance before Forlan almost latched on to a defence-splitting Simao pass.
Yet after an animated team talk from Benitez at full time, Liverpool were revitalised and deservedly doubled their advantage as Benayoun drilled a first-time half-volley into the bottom corner.
It felt like there was no way back for Quique Sanchez Flores's men, but they ignored the deafening noise to regain the ascendancy and ensure there would be one final twist.
Reyes collected a long pass, ghosted inside Glen Johnson and crossed for the unmarked Forlan to lash past Reina and send the travelling supporters delirious.
Atletico are now within touching distance of their first major European trophy since the 1962 European Cup Winners' Cup.