After a series of disappointing results, City now have only a mathematical chance of progressing to the knockout stages.
City have collected just two points from their opening four Group D matches and must win both their remaining fixtures - against Real and Borussia Dortmund, and hope other results go in their favour - to avoid premature elimination for a second successive year.
There are numerous permutations but the challenge facing City would seem an improbable one and manager Mancini has more or less admitted as much.
"It is finished," the Italian said. "I always believe in my team but now I think it is very difficult.
"We have two more difficult games left, which we have to try and win."
Nevertheless, the visit of nine-times European champions Real to the Etihad Stadium on Wednesday will be a glamorous occasion for last season's Premier League winners.
Midfield talisman Yaya Toure said: "We have to continue to work hard.
"We have a couple of chances against Real Madrid at home and go to Dortmund. We have a chance to qualify. We have a fantastic squad."