Mancini wishes he had moved to bolster his rearguard after captain Vincent Kompany was injured in the FA Cup fourth-round win at Stoke on January 26.
At the time City did not expect the 26-year-old's calf problem to require a lengthy lay-off but he has not played since and Mancini feels his absence has been a "big problem".
Despite Mancini stating on several occasions the Belgian is close to fitness, his return has continually been put back and he has now missed seven games.
He will not be risked for this weekend's trip to Everton and the next game against Newcastle in a fortnight, after the international break, is now being considered as the comeback target.
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 did 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."
City have also been without two other defenders in Micah Richards and Maicon through injury but their only major transfer activity in January saw striker Mario Balotelli leave the club.
Kompany's prolonged absence has raised fears he may require surgery or miss the rest of the season but Mancini continues to play down the seriousness.
He said: "He starts to run and we hope that he will be ready for Newcastle.
"He started with us three or four days ago but he was tired because he worked a lot.
"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.
With 19-year-old Matija Nastasic continuing to hold down a regular place, Joleon Lescott's appearances have remained infrequent.
Lescott was outstanding last season but his lack of game time this season was highlighted this week when he was overlooked for England selection.
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."
Mancini said the 30-year-old remains part of his plans and has continued to feature, if only off the bench.
He said: "You ask me about the national team? He didn't play one game in the last month. He always played."
Lescott made his first start in five games in the FA Cup quarter-final against Barnsley last weekend. In the three games between those starts he was actually an unused substitute twice but did feature once off the bench.
When asked if he could understand why he had been left out by England, Mancini said at a press conference: "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."
City face Lescott's old club Everton at Goodison Park this weekend needing to win to keep alive their slim hopes of retaining the Barclays Premier League title.
Mancini hopes David Moyes' men are still subdued after last weekend's shock FA Cup quarter-final loss to Wigan.
He said: "For them tomorrow will be important, for sure, because maybe they want to take Europa League.
City's 5-0 thrashing of Barnsley was their best performance of the season and Mancini agreed - "yes, I think so," he said - when asked if his team are getting stronger.
But with with a gap of 12 points at the top of the table, he still needs leaders Manchester United to tire.
He said: "Now, 10 games from the end, all the teams could be tired after eight months. We hope."