Despite a flurry of early chances, Pep Guardiola’s side were kept at bay by goalkeeper Thibaut Courtois.
A penalty that resulted in Bernardo Silva’s dismissal - and a resulting goal for Madrid on 20 minutes - furthered the challenge.
But City never gave up and eventually levelled on 41 minutes through Erling Haaland.
Vinicius Jr rounded the game off with the last kick of the game to hand the Spanish giants a 2-1 victory on the night.
The result means City bow out of the Champions League, however it was a valiant effort given the circumstances.
The Belgian winger explained that the players can be proud of the efforts they displayed as well as a round of applause for the fans, whose backing from the stands was electric.
“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.”
Watch the full interview at the top of the page...