Sergio Aguero's brilliant hat-trick secured the win while City, inspired by David Silva in midfield, could afford to see Carlos Tevez miss a penalty and still take three points.
Mancini said: "We had 15 chances in the first half and we scored only one goal - this is a problem because the game can change any moment."
He added: "Next time it's better if we close out the game in the first half.
"We need to improve because we have started the season very well but the season will be long. If we want to arrive at the end of the season still at the top we need to improve."
Wigan boss Roberto Martinez claimed his players had shown City too much respect.
Martinez said: "I am disappointed with the performance. We showed them too much respect.
"With the quality they have on the pitch and the size of the squad will allow them to be competitive in every competition but in one game you are only playing against 11 bodies.
"We played the occasion too much, we played their squad, when we only had to focus on the 11 players in front of us. We could have hurt Man City a lot more.
"From our point of view it is a real lesson but we still did a few good things that we are going to take into future games."
Source: PA
Source: PA