The three Napoli players were the subject of racist chants from some sections of the Fiorentina support during the game.
Koulibaly, who helped Napoli to a 2-1 win, was also targeted by spectators as he was interviewed on the pitch by DAZN after the game.
According italian press, Fiorentina's director general Joe Barone went to Napoli's changing room to apologise personally.
Koulibaly followed suit, revealing the fans called him a "f****** monkey".
"'Monkey of s***. F****** monkey'", Koulibaly's tweet began.
"They called me that. These people have nothing to do with sport. They must be identified and kept out of the stadiums. Forever."