The pair had to be separated by players and staff at the end of Milan's win against Parma.
Reflecting on the clash, Compagnoni said from the Sky Italia studio: "The scene is ugly, very ugly, and fuels doubts about Milan's choice, whether they did well to replace Fonseca with Conceicao. It's a scene that confirms the dressing room problems within Milan: many players had bad relationships with Fonseca. I think this confirms the problems of the group, perhaps due to the lack of a leader.
"The other issue is that the club is weak. I don't mean financially, but sportingly. If what happens happens, I'm also thinking of Leao and Theo, it means that the club is not particularly strong. And then there's the last doubt: whether Conceicao's choice was right or not."
Fellow reporter Paolo Assogna's opinion was along the same lines: "A sensational fall in style, we are talking about a club like Milan, there is a history and a brand to respect. It is a sensational fall in style and what happened is very serious.
"There was time to count to 10 to go and solve the problems somewhere else, as a football man should do. If I had to think with the head of a manager, or the owner, of Milan, I would be very annoyed."