Roberto Mancini was again left to rue a costly decision to deploy a three-man defence as the Spaniards tore into the hosts in the early stages. Karim Benzema struck after 10 minutes and Real should have had more in a devastating spell but City grew in confidence after switching formations and Sergio Aguero levelled from the penalty spot 17 minutes from time when Alvaro Arbeloa was sent off after tangling with the Argentine.
City poured forward in search of a winner in the closing stages but it was not to be and the result leaves them with just three points in Group D and unable to progress.
Joe Hart said City only had themselves to blame for their plight. He said: "We're very disappointed. We've had a few opportunities in this group when we could have done a lot better. All the games have cost us. We've lost our two away games and not won at home.We led in Amsterdam and led in Madrid. It's been a disappointing campaign. We've surprised ourselves in a very, very bad way in this competition."
The visitors went ahead early on as Benzema peeled away from Maicon to turn in a curling, deep cross from Angel di Maria at close range, despite City having plenty of players back in defence.
The goal typified what has been a hugely disappointing campaign for City, and Mancini admitted that his side had been below-par on too many occasions.
However, the home side dragged themselves level when referee Gianluca Rocchi pointed to the spot after 73 minutes when Edin Dzeko played in Aguero from a long Yaya Toure through ball.
Aguero went down after tangling with Arbeloa and what seemed a harsh decision was compounded for Real as the former Liverpool man was shown the red card. Aguero converted to level the scores.
"The first chance they had, they scored. We made a mistake. We were five against two in the box. When you concede like this it is always difficult," the Italian said.
"The first half we played so- so. We missed one or two chances. But we didn't lose tonight, we lost in the first few games – in Madrid we were 2-1 up with five minutes to go; in Amsterdam we were 1-0 ahead and missed some chances to close the game.
"I am disappointed like everyone else here at the club. We made some mistakes.
"When we started this group we knew it was going to be difficult. But we are a good team. You can lose against Real Madrid, Borussia Dortmund, but we are disappointed – we wanted to go through to the next stage. Now it's finished, we can do nothing."
Mancini also dismissed speculation that City may prefer to finish bottom of their pool following their final group match in Dortmund, rather than take third place ahead of Ajax and with it a place in the often-maligned Europa League. "We want to be in the Europa League, if it is at all possible," he added.
For Jose Mourinho, the Real Madrid coach, the stalemate meant his side would go into the last 16 as the runners-up in Group D behind Borussia Dortmund, but the Portuguese was unfazed by that prospect.
"The only two times I finished second in the group, I won the Champions League," he said. "It means something [to finish top], but my experience is, it doesn't mean so much."