The center back captained his country to a 1-0 World Cup qualification victory over Macedonia and was publicly criticized by the City boss for choosing to play so soon after recovering from a calf problem.
Mancini and Kompany then appeared to ignore each other when the 26-year-old was substituted during City's 4-0 victory against Newcastle on Saturday.
Asked if the two have spoken since the disagreement, Mancini told reporters: "No, for what? Vinny knows that his behavior was not good."
The former Inter coach denied, however, that there was a rift between the pair after reports had claimed that Kompany had not reacted well to Mancini's comments to the media.
Asked why they appeared to ignore each other as Kompany left the field, Mancini said: "I was happy because he played well. Kompany didn't have any problem."