The 2-1 win meant Real reached the quarterfinals 5-1 on aggregate. Vinicius Jr struck twice, once from the penalty spot after City captain Bernardo Silva was sent off for a deliberate hand-ball.
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“We’re disappointed,” Doku said.
“Even at 10 against 11 we did well, so we can be proud, but unfortunately we didn’t win.
“We gave our all and look you play against a big team like that and 10 against 11 and you’re still creating the problems, chances, so fair play to the players for their effort today.
“We were very happy with the fans today, they really pushed us, even when we were 10 against 11, they pushed us.
“Even after 1-0 they pushed us and it was a massive help for us, so I want to thank them.”