The punishment comes at a time when Tevez has been in fine form on the field having scored six goals in his last seven appearances.
With City facing Manchester United in an eagerly-anticipated derby at Old Trafford on Monday, Mancini is hopeful that run continues.
When asked if the community service was likely to cause a problem for City, Mancini said: "I don't think so, no. I didn't speak with him about this.
"I think that Carlos made a mistake and he will pay for this. But usually he has good behaviour."
Another City player, Samir Nasri, has also been banned from driving this week.
Mancini does not think these incidents badly affect the image of the club.
He said: "I don't think this. This is their private life. We can do nothing about this. This can happen sometimes."