Pablo Zabaleta went down with cramp before the end of thew 1-0 victory over Wigan that was their third match in seven days - with another demanding week ahead of the injury-hit Blues.
Super Spaniard David Silva scored the goal that keeps City on the heels of second-placed Arsenal and ahead of Premier League pursuers Chelsea and Tottenham to bring manager Mancini some relief.
The Blues boss said: “In the first half we played well and had three or four chances. The second half was very hard. We were very tired. The difficulty was that the players played three days ago.
“It was important that we won the game after we lost two points against Fulham. I have a team that for 28 games was either top or second. But when you have only 14 or 15 players fit it is very difficult.
“We have five days before the Kyiv game. The problem is that we are playing every three or four days. We go to Kyiv and play, fly back in the night, it is very difficult. But this is how it is for a top team.
“The players want to win every game, but sometimes it’s not possible. We haven’t the players available. But the situation is good because we have two cup games now that it’s important to get a good result in.”
The first leg of the Round of 16 Europa League tie against Dynamo Kyiv on Thursday is followed by Sunday’s FA Cup quarter-final at home to Championship side Reading.
Nigel de Jong came off the bench against Wigan after missing seven games with a damaged ankle, but Mancini said: “Nigel is not ready. He needs more time. I hope he can work for two days before Kiev, because he needs to work.
“I hope we can get three or four players back from injury, then for the Reading game we can change players.”
