He said that the Senegalese player was put on edge by the crowd's behaviour and that his red card "influenced" the outcome of the match.
The Napoli bossAncelotti pointed to that policy in an angry press conference following the match.
Napoli boss Carlo Ancelotti had said he asked the referee's assistant on three occasions to suspend the match due to the racist chanting, and that the next time his team would take matters into their own hands and walk off.
According to UEFA's protocol, the match should have been suspended at that point but instead the game was allowed to continue.
Match officials in Italy are expected to report racist incidents to public security officials who have the power to stop games.
"It shook him - he's a good-mannered player and he was bombarded by the stadium", added Ancelotti. "I think that in Italy we can do something more for this problem". Under Ancelotti's leadership the position of Napoli on racism and discriminatory abuse is clear, we note that the club previously threatened to take their players off the pitch before a match against Atalanta on December 3.
'It was impossible for him to be calm - he cares a lot about the issue of racism and he commits a lot of time to the matter, including in society.
"What happened today is not good not only for us but also for Italian football as a whole", the former Chelsea and Real Madrid manager continued.More news: Ashwin in doubt for MCG Test
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Cardona said he will request that Inter fans be banned from traveling to away games for the rest of the season and that the northern end of the San Siro, where Inter's "ultra" fans are based, be closed until March 31.
Milan police chief Marcello Cadorna told journalists that the incident happened after around 100 Inter fans attacked Napoli supporters' minibuses with chains and hammers.
He tweeted: "There's no place for racism in football". Milan police were not immediately contactable when called by CNN International.
"Monkey chants" were heard throughout the match from the Inter support in his direction and Koulibaly was eventually sent off after receiving two yellow cards - the second for sarcastically applauding referee Paolo Silvio Mazzoleni - after the 80th minute, with the home side eventually seeing out a 1-0 win against the 10-men.
Substitute Lautaro Martinez then scored a stoppage-time victor for Inter, while Napoli finished the game with nine men after Lorenzo Insigne was also sent off.
"I'm disappointed by the defeat, but above all at leaving my brothers!"
Koulibaly apologised on Twitter for being sent off, though adding: "I am proud of the colour of my skin".