Renan Lodi headed the only goal at Old Trafford to edge Atlético into the last eight.
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Renan Lodi struck in the first half and Atlético's defence held firm in the second as Diego Simeone's men won at Old Trafford to progress 2-1 on aggregate in this round of 16 tie.
13': Oblak denies Elanga with head from close range
16': De Gea claws away deflected De Paul effort
41': Renan Lodi heads in from Griezmann cross
59': Sancho thunders volley over for home side
77': Oblak parries Varane's header away
Match in brief: United fall to textbook Atlético
The two goalkeepers took centre stage in a first half high on endeavour but low on chances, Anthony Elanga being denied by the head of Jan Oblak from a low Bruno Fernandes cross before Rodrigo De Paul's deflected shot was pushed away by David de Gea.
João Félix did have the ball in the net for the visitors but Marcos Llorente had strayed offside before teeing up the Portuguese striker. It proved a temporary reprieve for the Red Devils, though, as João Félix's back-heel released Antoine Griezmann, who stood up an inviting cross to the far post for Renan Lodi to head in.
Ralf Rangnick's men increased the pressure after the break and nearly levelled when Jadon Sancho's ferocious volley fizzed just over. Raphaël Varane thought he had forced extra time with a thumping header from Alex Telles' free-kick but Oblak continued his stunning resistance as Atlético dug in to see out the remaining time.
PlayStation® Player of the Match: Koke (Atlético)
"Koke is the leader on the pitch. He not only organises and balances the team, he also sets up the attack playing in between the lines and finding the gaps. Although he left the pitch in the 80th minute with an injury, he made the difference today in every sense. After he left the pitch Atlético missed his direction."
UEFA Technical Observer panel
Richard Martin, Man. United reporter
United started well but could not find anything to show for it and they soon paid for their early exertions, tiring and ceding more ground to Atleti. Once they conceded, they never really looked like getting back into the game, doing plenty of huffing and puffing yet rarely truly troubling the Rojiblancos. In truth they did not really deserve to win either leg and can have no real complaints with their exit.
Joe Walker, Atlético reporter
About as vintage a European display as it gets from Atlético under Simeone. Dogged, determined, keeping their opponent at arm's length, frustrating the life out of them and hitting them on the break when they least expect it. Brilliant from the visitors, who you have to say over the two legs deserve their place in the last eight.
Koke, Atlético midfielder: "It's important for us to still be in the Champions League in what's been an up and down season. We deserved the win in the first leg but fought so hard here to get what we deserved from this tie. For me, Oblak is the best goalkeeper in the world. He's shown it once again tonight."
Rodrigo de Paul, Atlético midfielder: "We played a great game. We suffered when we had to and hit when we had the chance, here at a great stadium against a great team. It was an even game. We knew we'd suffer, but we also knew we'd get our chances on the counter and we took one of them."
Héctor Herrera, Atlético midfielder: "We're really happy. We knew it would be tough and they'd control the ball more than they did in the first leg. We knew how we could hurt them, and that's what we did to create a few goalscoring chances. We knew how to suffer, to be regimented, and that's what has seen us go through."
David de Gea, Manchester United goalkeeper: "We are really disappointed with the result. We did not do enough in both games to win it. They are a team with a lot of experience. They know how to play those Champions League games. They scored a goal then are a tough team so it was hard for us to create chances."
Rio Ferdinand, BT Sport
"Credit to Atlético. Everyone says they are not the team of the last few years but their manager knows how to put out a team to do a job. They were so clever in the little details. Really good team performance, getting back into position and everything motivated by the team."
- Manchester United have won only two of their last 15 matches in the Champions League knockout phase (D4 L9).
- The Red Devils have lost four of their last five home games in the Champions League round of 16.
- United had scored in their last 13 Champions League matches before this game.
- Atlético ended a run of five Champions League matches without a win against English clubs (D1 L4).
- Griezmann has been involved in six of Atlético's nine Champions League goals this season (four goals and two assists).
- Atlético have scored the first goal in seven of their last eight away games in all competitions.
Renan Lodi – 13
Stefan Savić – 9
Antoine Griezmann – 7
Man. United: De Gea; Dalot, Maguire (Mata 84), Varane, Alex Telles; Fred (Cavani 75), McTominay (Matić 67); Elanga (Rashford 67), Bruno Fernandes (Pogba 67), Sancho; Ronaldo
Atlético: Oblak; Savić, Giménez, Reinildo; Marcos Llorente, Herrera, Koke (Kondogbia 80), De Paul, Renan Lodi; João Félix (Felipe 90), Griezmann (Correa 90+3)