City managed a 1-0 win over Bolton on Saturday thanks to an early goals through Carlos Tevez.
“I’m happy because we won this difficult game, but I think that we must improve these situations,” said Mancini.
“It’s a little bad luck, but we need to improve. Sometimes we’re too selfish, but I’m happy because I think we played very well.
“We didn’t concede any chances in the first half. I think at the moment Bolton are one of the form teams. They have a fantastic manager.
“I think we maybe had 50 chances to score, but that’s football. We must improve in this situation.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.