Spalletti’s side won 1-0 on Wednesday but Napoli boss Carlo Ancelotti asked the San Siro showdown to be suspended three times because of the monkey noises heard around the grond.
Koulibaly was sent off after a second yellow card before Lautaro Martinez netted a late winner in stoppage time.
Lorenzo Insigne also saw red for the visitors but the match was overshadowed by the racism towards Koulibaly, who said after the match:
‘I am proud of the colour of my skin. Proud to be French, Senegalese, Neapolitan: Man.’
And Inter boss Spalletti did not hold back when asked about the chants, claiming Italian football needed to change.
‘Racist chanting should not be taking place,’ he .
‘If 65,000 people come and watch the match on Christmas, they want to see something else. This is the football that Italians and the people around the world want to enjoy.
‘People want to find football a pleasant place to be together, this is the change of mentality we have to make.
‘This is the right thing to do because our objective is to bring our football up to the top in Europe.’
Inter’s win saw them move to within five points of second-placed Napoli and Spalletti was pleased with how his side performed.
‘I saw a strong Inter tonight, from the beginning to the end. In many ways, we deserved to win,’ he said.