Kompany was controversially sent off in last week's win at Arsenal for a challenge on Jack Wilshere. The decision of referee Mike Dean to dismiss him was widely criticised and overturned after a successful appeal by City but, although Kompany was not in the wrong, Mancini feels he should temper his approach.
The 26-year-old was also dismissed for a similar challenge in a game against Manchester United last season and the City boss does not want to keep losing his skipper. Mancini said: "He's a defender. Sometimes when the defender is under pressure he can do a bad tackle but I think he needs to pay more attention, because this has happened two times."
He added: "We can have a problem if we have another situation like this. I spoke with Vinny and told him to have more attention on his tackles."
Mancini does not personally have a problem with Kompany's technique or necessarily think it needs changing but, as the player did lunge towards Wilshere, he fears how referees might judge certain tackles.
Asked if he feared Kompany would lose his enthusiasm for tackling as a result of his request, Mancini said: "No, no, I don't think this but there are some situations that he can go, because like against Arsenal sometimes the referee can do a mistake, like the players.
"It is possible, like against Arsenal, the referee sees a different view from us and Vinny. Every tackle can be dangerous, it depends on the situation but this is football. I told him to pay attention and that it is better you don't go sometimes. You wait and don't do a tackle - it is better. I think probably he won't change his style but if he has more attention in some situations it is better."
The Kompany issue has prompted a debate on whether the art of tackling is being lost as a result of modern interpretations of rulings that protect attacking players.
Mancini hopes players are not too timid to tackle in future.
The Italian, a striker in his playing days, said: "This is the English style. This is impossible (to stop). Sometimes when you have strong tackles here, in Italy sometimes it would be a foul - but here no. Sometimes this is good. It is normal that the players continue to do a tackle."