The Spanish side earned a shock 3-2 victory at Anfield to go through 4-2 on aggregate, after having won the first leg 1-0 at home about two weeks earlier.
After falling 2-0 down on the night, substitute Marcos Llorente struck twice in extra time.
Alvaro Morata added a late third to ensure a famous victory for Diego Simeone’s side against a Liverpool team unbeaten in their last 25 home games in European competition.
Liverpool broke through two minutes before half-time when Alex Oxlade-Chamberlain burst to the byline.
He pulled back a cross to Georginio Wijnaldum who powered an angled header into the bottom corner.
After the interval, Liverpool peppered Atletico Madrid goalkeeper Jan Oblak but the Spaniards survived.
They almost pulled off a last-minute shock when a header from Saul Niguez was ruled out for offside.
Liverpool took the lead in the tie four minutes into extra-time, with Roberto Firmino heading against the post and then driving home the loose ball.
Yet then it all went wrong for Juergen Klopp’s side —– a dreadful pass out from goalkeeper Adrian straight to Joao Felix, gifted Atletico the ball.
Llorente punished the Liverpool goalkeeper for his error with a precise shot into the far corner.
Llorente then produced a carbon copy finish as Liverpool’s defence backed off following good work on the counter from Morata.
This effectively ended Liverpool’s hopes of defending their European crown.
Morata put the icing on the cake in the final moments after a breakaway.(Reuters/NAN)