The home side halted Carlo Ancelotti's perfect league start with a 1-0 victory thanks to a Carlos Tevez strike in the second half.
And Mancini has lauded his team after they managed to successfully shut down a dangerous Chelsea attack that had previously blown away all before them this season, but warned his team they would need to improve.
"After five games they scored 22 goals. Chelsea is a fantastic team. I think our guys today played a strong, strong match," Mancini told Sky Sports after the match.
"I think we must work to improve always. Everyday. But today we played against Chelsea, for this we must pay attention."
Mancini believes his side's cautious approach was justified but he was quick to point out that his team can also play good football when they need to.
"I think with all the strong teams like Chelsea, it is hard to find space, it is difficult," he added.
"I think we closed all the space for them and when we had the chance we played football always.
"This is important. And when we had the chance to score we scored."
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