AC Milan said it was "surprised by the total lack of consultation" after Serie A installed a painting featuring monkeys at its headquarters for a league-wide anti-racism campaign.
Roma also said it "was very surprised" by the move.
"We understand the league wants to tackle racism but we don't believe this is the right way to do it," Roma tweeted.
While black players are regularly subjected to monkey chants in games, artist Simone Fugazzotto said his painting featuring three monkeys to represent three different races was meant "to show that we are all the same race."
"Serie A decided that every year it will have a different artist interpret the damage caused by racism," the league added. "Simone Fugazzotto, a witness to the whistles at Koulibaly at the San Siro, made a provocative work in which the monkeys are actually the racist fans."