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.
"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."
Mancini said he was pleased with Tevez's performance despite the Argentinian, who had seemed odds on to leave City in the summer, not being fully fit.
"Carlo is not 100% at the moment but I am happy for him because for me he played very well with Sergio, he missed a penalty but this can happen - usually he scores," said Mancini.
"It was important for him to start, to play and to play well and maybe in two or three games he will be 100%."
If Aguero was the sponsors' man-of-the-match it was Silva who pulled on the strings, but Mancini refused to pick out any of his players for special mention.
He added: "Silva is a top, top player but so is Aguero, so is Yaya Toure, so is Nasri - for them it is easy to play football."
Mancini is hopeful that Gareth Barry will be fit to return for City's Champions League debut against Napoli on Wednesday - and that the rest of this players have recovered from international duty.
"I hope we will have Gareth back for Wednesday, we have no other injury problems but they are so tired as they all played two games for their national teams and we need to recover in the next three days."
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."