Marcos Llorente struck twice in extra time as Atlético stunned Liverpool at Anfield.
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Marcos Llorente produced two sucker punches in extra time to turn defeat into progression for Diego Simeone's men.
The match at a glance
Jan Oblak, in his 50th UEFA Champions League match, made several early saves but Liverpool's persistence was rewarded just before half-time when Alex Oxlade-Chamberlain's cross was headed in by Georginio Wijnaldum.
Jürgen Klopp's charges were relentless after the break as Oblak denied Oxlade-Chamberlain and Firmino before Andy Robertson nodded against the bar. Sadio Mané and Mohamed Salah also went close but the visitors held on to force extra time.
Atlético's resistance did not last much longer as Firmino converted after his header came back off the post. However, from being seemingly down and out, the visitors turned the tie around. Llorente curled past Adrián twice in nine minutes and Álvaro Morata ran clear in the dying seconds to add a third.
Man of the match: Jan Oblak (Atlético)
Gareth Southgate, UEFA technical observer: "An outstanding display with the goalkeeper producing several important saves and making composed decisions under pressure."
View from the stadium: Matthew Howarth, Liverpool reporter
Liverpool could not have done much more against Simeone's side. The hosts arguably should have been out of sight long before Firmino made it 2-0, but try as they might they could not get the better of Oblak in the second half of normal time. Credit must go to the visitors, who defended doggedly before taking the chances that fell their way in extra time.
Visitors' view: Joseph Walker, Atlético reporter
I can safely say when Firmino scored to make it 2-0, I didn't expect to be writing this. That was some smash and grab. They hung on for dear life, their goal living a charmed existence, but somehow Atlético are not only through but they have also beaten Liverpool at Anfield. It wasn’t pretty, it was dogged and determined, but enough to get the job done.
Marcos Llorente, Atlético midfielder: "We don’t have any limits to how much we can go through and suffer. We defended with our lives and when we all pull in the same direction, these things can happen."
Diego Simeone, Atlético coach: "I’m very happy for the side and the club. We're back in the best eight sides in Europe and have beaten an extraordinary opponent. They were brilliant, with their crowd pushing as they did, but we were able to come through it. We never gave up with their second, we got it to 2-1 and we felt something inside us when that went in."
Jordan Henderson, Liverpool midfielder: "We were really disappointed with that result. I thought overall our performance was good, our intensity was good as we spoke about before the game. We put everything into that game so we are bitterly disappointed especially with the goals we conceded. We were largely pleased with our performance tonight but those goals were disappointing."
Jürgen Klopp, Liverpool manager: "I am completely happy with the performance. It’s so difficult to play a side like this. We know in the last two years we had some lucky moments in the Champions League. You have to, to reach two finals, but today it was everything was against us in the decisive moments."
- Atlético ended Liverpool's 25-match unbeaten home run in European games (W18 D7).
- This was Klopp's first defeat in a two-legged knockout tie as Liverpool manager after ten successive victories.
- Atlético have won their last five two-legged knockout ties against English clubs.
- Wijnaldum has scored four goals in his last five UEFA Champions League appearances at Anfield.
- Marcos Llorente scored twice in a game for the first time in his career.
Liverpool: Adrián; Alexander-Arnold, Gomez, Van Dijk, Robertson; Henderson (Fabinho 106), Oxlade-Chamberlain (Milner 82), Wijnaldum (Origi 106); Salah, Firmino (Minamino 113), Mané
Atlético: Oblak; Trippier (Vrsaljko 91), Savić, Felipe, Renan Lodi; Koke, Saúl Ñíguez, Thomas, Correa (Giménez 106); João Félix (Morata 103), Diego Costa (Llorente 56)