Koulibaly, who made a decisive goal-line clearance to deny Inter captain Mauro Icardi, had monkey noises directed at him throughout the match at San Siro stadium.
The game was marred by racist chanting towards Napoli centre-back Kalidou Koulibaly, with the away side asking for the match to be halted after the 27-year-old Senegalese global was repeatedly subjected to monkey noises.
A host of other famous names and faces also showed their support, including Juventus' 5-time Ballon d'Or victor Cristiano Ronaldo, who posted to Instagram: "In the world and in football I always want education and respect".
"We need to be more cunning", added Spalletti who has also seen his side twice throw away the lead in a 2-2 draw at AS Roma and lose 1-0 at leaders Juventus despite creating more clear cut chances.
Lega Serie A announced on Thursday that Inter's next two home games will be played behind closed doors, while the Curva Nord - a section reserved for the club's "Ultras" - will also be closed for a third fixture.
Koulibaly was dismissed in the 81st minute after he was first booked for a foul on Matteo Politano and was then shown a second yellow card for sarcastically applauding the referee's decision.
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And he's received support from his peers, with Cristiano Ronaldo showing support with an Instagram post.
Milan mayor Beppe Sala, an Inter supporter, said on Facebook that the next time he hears racist chanting at the San Siro he'll stand up and leave.
"The player's (Koulibaly) nerves were shaken, he was nervous". "It's not good for us and it's not good for Italian football".
'The task of the state must be to curb it, but we also have government representatives who incite racial discrimination, divisions based on skin colour and geographical origin.
"I am sorry for the defeat and for the fact that I left my brothers. To be French, Senegalese, Neapolitan: Man".
Reports claim the incident happened at "around 18:30 GMT", an hour before the game kicked off of their inaugural Boxing Day fixtures and he's since been identified as Daniele Belardinelli, a 35-year-old Inter ultra from Varese.