City continued their unbeaten start to the season with a 3-1 victory over Queens Park Rangers, but a Bobby Zamora goal continued a run without clean sheets so far in 2012-13 for the reigning champions.
Mancini also said that he wants his side to be more clinical at the other end to take the pressure off his defence.
He told ESPN: "I said it is important that we improve because we can't concede a goal in every game.
"I think we played well in first half but we have one problem at the moment and that's that when we have a chance to score we don't.
"In the second half we did not play well but in the end it is important we take the three points."
City will continue their title defence after the international break with a trip to Stoke City on Saturday, September 15.