Despite boasting one of the best defensive records in the Premier League, the champions and new competition leaders have lacked their usual solidity this season.
Criticism increased after City conceded twice at corners in a damaging 2-2 Champions League draw with Ajax a fortnight ago and then allowed Tottenham to score from another set-piece in their next match.
Their zonal marking system was highlighted as a possible factor, but Mancini believes Saturday's 5-0 win over Aston Villa - a fourth clean sheet in six Premier League games - points to a better way forward.
He said: "We have worked on set-pieces for some time.
"We conceded because we don't want to do something more to cover - maybe one metre more.
"Sometimes we are so lazy for this. Instead, if we pay attention we are able not to concede a goal.
"Against Tottenham, it was a difficult match.
"When you have ball possession - Tottenham for 20 minutes did nothing and then the first set-piece they score.
"Like against Ajax, there are these moments.
"But after their goals we started to play, we scored two goals (in both of those games).
"Against Villa we lost in the Capital One Cup, 4-2. We had big problems.
"Saturday I think we played very well and to score five goals is not easy, never."
City enjoyed a good weekend as the victory over Villa, coupled with Manchester United's surprise loss at Norwich, took them to the top of the table for the first time this term.
Their position was further strengthened as third-placed Chelsea lost to West Brom.
It puts City in good heart for a week in which they play Real Madrid in the Champions League and then travel to Chelsea.
Mancini said: "We wanted one game where we could be so quiet on the bench and for the last 20 minutes it was like this.
"It was important we did a performance and played very well at football.
"I think this is important this for the Barclays Premier League and, it is clear, it is better to prepare for the next game with a game like this.
"But Wednesday will be a different competition and I think it will be hard.
"It is a fantastic week for us and the club and the supporters."