City conceded two goals for the fourth consecutive competitive game in a row as they drew 2-2 with Liverpool at Anfield.
Mancini admitted that they need to cut out mistakes at the back, and quickly, in order to have continued success.
He said: "This is the time to finish conceding two goals every game, but we have taken one point when we went down two times.
"We started with the ball for 30 minutes, we had it in their half and had four or five chances to score.
"But we conceded a goal from a corner and something changed."