The Turkish club were handed a boost when Sergio Ramos was sent off for the hosts after 26 minutes of the UEFA Champions League clash at the Bernabeu but still fell behind to Gareth Bale's free-kick eight minutes before the break.
Umut Bulut drew the visitors level within two minutes but their challenge stalled in a lacklustre second half as goals from Alvaro Arbeloa, Angel di Maria and Isco left the Turkish side needing a win over Juventus in the final group game to qualify.
And a disappointed Mancini could only reflect on a poor defensive display, particularly after the break.
"Real Madrid players (are of a) very high standard and if we grant opportunities as we did, we cannot win," he said.
"I do not know what happened, I have to look at it more closely. After the first period I was very confident.
"I know we have a problem in defence. I think we have to work more, we cannot fix everything in one month.
"With the mistakes we made was very difficult to win. We were very well prepared this match, the first period was perfect.
"The second, I do not know, I have to talk to the players to understand what happened."
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