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.
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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.”