Kompany's red card was later rescinded, meaning he can play in Saturday's home game against Fulham.
"I think he needs to pay more attention because this has happened two times," said Mancini. "We can have a problem if we have another situation like this. I spoke with Vinny and told him to pay more attention to his tackles.
"It's better that you don't go in sometimes. You wait and don't do a tackle. I think probably he won't change his style but if he pays more attention in some situations it's better.
"Every tackle can be dangerous, it depends on the situation. Against Arsenal the referee had a different view from us and Vinny."