Roberto Mancini claims Maurizio Sarri "offended many people" with his remarks during Napoli's Coppa Italia defeat to Inter.
The Inter boss accused Sarri of using racist and homophobic slurs towards the end of the quarter-final, which was decided by goals from Stevan Jovetic and Adem Ljajic.
Sarri apologised after the match and insisted he was unaware of what he may have said during a heated exchange, but Mancini says a number of people would have been upset by the comments.
"Those phrases didn't offend me but they've offended many people who are teased and mocked every day with jibes like this," he told Ansa.
However, Renzo Ulivieri - the head of Italy's Football Managers' Association - insists he does not consider Sarri to be a racist and plans to hold clear-the-air talks between the two.
"It was a scrap between two coaches, but at the end of it, Sarri apologised immediately, both publicly and directly to Mancini," he said to La Stampa.
"Sarri is not a racist. A man who was speaking in difficulty, but calmly, acknowledged he was wrong.
"In the coming days I will speak with them. I know them, they are two decent people. I will gladly offer myself as peacemaker."
A decision on grounds for a potential punishment for Sarri is expected on Thursday.