City have conceded an alarming number of goals in such a manner this season, and did so again against Tottenham on Sunday before fighting back to claim a 2-1 win.
Some of the blame has been pinned on the zonal marking system which details players to take charge of areas, rather than players, but Mancini said: "We are not strong enough to mark man-to-man, and every time we do there is a risk of conceding a penalty. If we work, we can improve the system. We have let in goals because of it, but we can change that. We are working on it, but we need to work more."
Sergio Aguero levelled Steven Caulker's first-half header but it took yet another late goal from Edin Dzeko to seal the win.
The Bosnian's well-taken 88th-minute effort was his seventh of the season, six of which have come from the bench.
It only enhances Dzeko's reputation as a super-sub, even if it is one both he, and his coaches, bristle at.
"We can only pick 11 players," said Blues assistant boss David Platt. "We have a lot of players who would play in almost any other Premier League team. Edin is one of those players.
"We felt we needed an injection. We needed a little bit more height to get a platform to hold the ball up.
"We also know he is a goal threat and he is fresh.
"He has scored lots of goals this season and since he has been here he has scored some heavy goals."