Real went ahead after 10 minutes when Karim Benzema was left unmarked and in space to score with the goal at his mercy, but City, outplayed in the first half, improved in the second and equalised with a Sergio Aguero penalty after 74 minutes.
Real defender Alvaro Arbeloa was sent off for fouling Aguero and conceding the penalty which the Argentine swept home having missed a golden opportunity to score in the 65th minute when Iker Casillas made a point-blank save.
Real's only disappointment might be qualifying as runners-up in the group after Borussia Dortmund grabbed top spot with a 4-1 win at Ajax Amsterdam.
"We wanted to fight for first place but it was not to be but the important thing is that we are through," Casillas said in an interview with Spanish TV.
"We missed a few chances to end the match as a contest in the first half but the truth is we were up against a great team.
"It's also true that we felt a bit discriminated against by some of the referee's decisions. But we'll focus on the positive which is that we are through to the next round."
Real ripped City's three-man defence to shreds until coach Roberto Mancini changed his formation to four at the back with Aleksandar Kolarov dropping deeper after half an hour.
Real's opener came after some suicidal defending by the English champions when Maicon failed to stop Benzema running in on Angel di Maria's cross.
Mancini's men were left ruing another early exit after their Champions League debut appearance last year ended at the same stage.
"We've had a few opportunities in this group where we could have done a lot better," City keeper Hart told Sky Sports television.
"All the games have cost us - we've lost our two away games and not won at home. We led in Amsterdam and we led in Madrid so it's been a bad campaign for us."
