The Belgian skipper was dismissed for a heavy tackle on Jack Wilshere in Manchester City's 2-0 win at Arsenal last week, but saw his three-match ban overturned on appeal.
Kompany was shown two red cards last season, including one in a Manchester derby FA Cup defeat, and the Italian has warned his skipper that he must "pay more attention" to his tackling.
“Vinnie’s a defender and sometimes when a defender is under pressure he can do a bad tackle," Mancini told reporters. “I think he needs to pay more attention, because this has happened two times.
“We can have a problem if we have another situation like this. I spoke with Vinny and told him to have more attention when he tackles. I told him to pay attention and that it’s better that you don’t go in sometimes. Sometimes, if you wait and don’t do a tackle, it’s better.”