The Spanish champions bowed out of Europe’s premier club competition at the round of 16 stage for the second straight season by suffering a 4-2 aggregate defeat to Pep Guardiola’s men, with Varane the villain for Zinedine Zidane’s boys with two costly errors.
Varane lost possession in his own penalty box for the hosts’ opener in the ninth minute and following Karim Benzema’s equaliser, the France FIFA World Cup winner’s attempted pass to goalkeeper Thibaut Courtois was intercepted by Gabriel Jesus, who drilled in City’s winner in the 68th minute.
It capped a rare bad evening for Varane, who was without his usual defensive partner Sergio Ramos, who missed the game through suspension, with Eder Militao debutising in his absence.
"This defeat is mine. I have to assume that. This defeat is my responsibility," Varane told Movistar.
"We prepared well for it, but mistakes cost you. I can't explain the mistakes - it can happen in football.
"I'm sad for my team-mates. Until the 1-1, we had a chance to go through and today it didn't go well.
"This has not happened to me very often before. You have to have character to come back stronger."
After defeating Real Madrid, Manchester City will face Olympique Lyon in the quarterfinals in Lisbon next week.
