The Premier League champions have been without their influential captain Vincent Kompany since he suffered a calf injury in the FA Cup win at Stoke seven weeks ago.
Second-placed City head to Everton in Saturday's lunchtime Sky Live showdown desperately needing a victory to reduce the 12-point gap between themselves and neighbours United.
Reflecting on the frustrations of Kompany's stuttering rehabilitation, Mancini said: "Probably we made a mistake because when we knew of this problem we were four days to the close of the market.
"Probably then we should maybe have bought another defender. Also, last year he had this problem, for one month he didn't play. This is a big problem. For me we made a mistake in this case.
"We had a chance because we had one good defender but we didn't think that Vinny would stay out for 40-45 days."
The Italian manager is hopeful his Belgian centre-half will be fit for the Newcastle clash in a fortnight, although the prospect of required surgery remains a threat
"He has started to run and we hope that he will be ready for Newcastle," Mancini added. "His calf was tired but he didn't have any problems.
"But we don't want to take a risk at this moment because we have one game and after it is the international break. It is better we wait."
Kompany's absence has seen Kolo Toure, fourth-choice centre-back earlier in the season, return to form and prominence with four successive starts.
The player who seems to have missed out is Joleon Lescott, whose lack of game time cost him his place in the England squad this week.
Mancini said: "I love Joleon Lescott. Seriously, because Joleon is a top-quality man and a serious, serious professional player.
"He is perfect as a man and as a player. After I can decide if he stays on the bench but this is another story."
When asked if he could understand why Lescott had been left out by England, Mancini said: "I don't know. But I read all the newspapers pushed for Rio Ferdinand.
"One manager should take a decision, he has a lot of defenders. I don't know but Joleon is a good player."