Romelu Lukaku was subjected to monkey chants from the crowd during Inter Milan's 2-1 Serie A victory over Cagliari on Sunday.
The chants could be heard before and after the striker scored a penalty to win the game in the 72nd minute before he looked towards the Cagliari supporters.
The 26-year-old sent goalkeeper Robin Olsen the wrong way with 20 minutes remaining to mark his second goal in as many games for his new club.
Inter boss Antonio Conte said after the game: "I really didn't hear anything from the bench. However, it is true that in general in Italy more education is needed."
The former Chelsea head coach added: "I have also heard (Carlo) Ancelotti complain about the constant insults received on certain pitches. When you are abroad there is more respect, the fans think only of supporting their team."
Former Juventus striker Moise Kean, as well as midfielder Blaise Matuidi, were subjected to racist chanting from Cagliari supporters during a Serie A clash last April.
The league's disciplinary panel later decided not to take action against the club.
Inter lead Serie A after two games on six points along with Torino and champions Juventus, while Cagliari have yet to pick up a point.