City were ahead on two occasions at the Bernabéu, with Edin Dzeko handing Mancini’s men the lead in the 69th minute before Marcelo levelled for Madrid.
With five minutes remaining, Aleksandar Kolarov’s free-kick appeared to have sealed three points for the visitors, but Karim Benzema equalised before Cristiano Ronaldo netted a 90th minute winner.
In the immediate aftermath of losing their Group D opener 3-2, City goalkeeper Hart admitted his frustration at twice squandering a lead against the Spanish champions.
“We blame ourselves. We don’t credit Real. They are a very good team, but we got a lead twice and lost it,” Hart told ITV.
“We dug deep, got a lead twice and we lost it, so we can only blame ourselves.
“It’s hard to come off the field after losing 3-2 and be positive. I’m really sorry.
“We’re not a team that should come here and pat ourselves on the back for doing well. We’re a team that gets results.”
However, in a news conference shortly after, Mancini chastised Hart for the goalkeeper’s comments about City’s display.
“Joe Hart should stay in goal and make saves.” Mancini said.
“If anyone should criticise the team it should be me, not Joe Hart. I am the judge, not Joe Hart.”
The 47-year-old conceded he was disappointed with City’s defending, and the Italian was particularly upset to see the English champions fail to see out the victory with just three minutes remaining.
“I don’t want us to continue to defend like this, and we did a mistake like that.” Mancini added.
“When it was 2-1, we should have continued to play high like we did in the second half.
“We wouldn’t have conceded if we hadn’t been so deep. We should have had more courage at this time.
“It’s difficult to take, but not because we lost.
“You can lose against a team like Real Madrid, especially in the Bernabéu, but it’s difficult to take because with three minutes to go we were 2-1 up.”