Adriano Galliani is keen for his players to approach the referee when subjected to abuse by fans, while Fifa would not condone the full-back's actions
In a similar scenario to what happened to Kevin-Prince Boateng at the start of 2013 in the winter break, the Milan full-back reacted to a torrent of abuse in a friendly match, however the whole team did not follow him this time.
Rossoneri CEO Adriano Galliani believes the abuse was disgraceful, but felt his player reacted in the wrong way when the incident occurred.
"The racist chants are unspeakable and outrageous, but he shouldn't have left the pitch," Galliani told Sky Sport.
"Although it was terrible behaviour by the crowd, the rules are for the player to go to the referee. He then goes to the fourth official, who alerts the police officers. The game is then suspended.
"You cannot leave the pitch."
Milan subsequently released a statement reiterating their desire to see their players speak to the referee before storming off the field of play in future.
It read: "This was not a decision he [Constant] should have taken upon himself to make.
"And, despite his more than understandable reasons and the anger he must have felt, AC Milan would like to remind everyone that the only people responsible for intervening against any manifestations that offend the human dignity, which includes racial discrimination, are the referee in charge of the match and the head of public safety."
Fifa also wanted to stress that, though the organisation want to see racism stamped out of football, walking off is not a viable solution for players.
"Fifa is monitoring the situation and awaiting the result of the investigation launched by the Italian FA," it said in a statement to Omnisport.
"Fifa's position on the issue of racism is unequivocally clear: there is no place in football for racism or for any form of discrimination.
"As stated by the Fifa president [Sepp Blatter] after the incident involving Kevin-Prince Boateng in January, if a player walks off the pitch because he has been racially abused, it is a strong and courageous signal, but it cannot be the solution in the long term.
"We have to find other sustainable solutions to tackle the problem at its roots."