A goal from Carlos Tevez - his 10th of the season - in the fourth minute was enough to separate the sides and though Mancini was pleased they kept the pressure on the leaders he despaired at the number of chances that went begging.
He said: "You can say we had some bad luck but we must improve. Sometimes we are too selfish. We had maybe 15 chances to score. When you have a lot of chances you think the game is easy."
Mario Balotelli and David Silva both saw efforts come back off the woodwork at Eastlands.
Mancini continued: "You shoot when it is better to pass the ball. We must improve this situation. It means you can draw when you should have won by three or four goals. It was the same at Stoke where we deserved to win but we drew. When we have a chance we must score. If I had played, I would have scored two or three goals."
Despite his goal, which came after Gary Cahill failed to cut out a through ball from Yaya Toure, Tevez seemed ill at ease and he picked up his fifth booking of the campaign - meaning he will miss the match against West Ham on Saturday.
So too will Aleksander Kolarov who is also banned after being dismissed by referee Andre Marriner for picking two yellow cards.
Tevez ended the game by giving Mancini an ear-bashing when he was replaced by James Milner in the final minute.
Mancini shrugged off the incident and said: "I am happy about this. I would like all players to be like Carlos and want to stay on the pitch. I needed a player like Mario on the pitch as he is taller than Carlos. We must continue to score when Carlos doesn't play."
Kolarov was dismissed by referee Andre Marriner after a challenge on Sam Ricketts and Mancini, who saw Kolo Toure limp off with a calf injury, added: "I did not agree with that decision. It was not right."
Source: PA
Source: PA