Zinedine Zidane’s side were trailing 2-1 from the first leg at the Santiago Bernabeu and went behind at the Etihad Stadium to a Raheem Sterling goal.
Karim Benzema netted in the first half to cancel out Sterling’s early opener, before Gabriel Jesus struck in the second half to ensure Pep Guardiola’s side qualify for the quarter-final.
However, City’s two goals came after errors from Varane, who was exposed at the defense in the absence of suspended centre-back partner, Sergio Ramos.
“This defeat is mine, I have to accept it,” Varane told reporters after the game.
“I’m responsible for this defeat. We had prepared well but you pay for your mistakes. I’m sad for my team-mates.
“At 1-1 we had the chance to qualify and today things didn’t go to plan.”
