The Nerazzurri claimed a 1-0 Serie A win over Carlo Ancelotti’s side thanks to a last-gasp goal from Lautaro Martinez.
After the match, Ancelotti said they requested the match be suspended three times due to fans directing offensive chants at Koulibaly.
Ancelotti claimed there were three separate warnings issued in the stadium but that the abuse continued regardless.
On Twitter, Koulibaly, who was sent off in the closing stages, told his followers that he is “proud” of his heritage and of being part of Napoli’s footballing culture.
“I’m sorry for the defeat and above all for having left my brothers!” he wrote.
“But I’m proud of the colour of my skin. Of being French, Senegalese, Neapolitan: man.”