Romelu Lukaku has demanded immediate further action be taken to tackle racism in football and says "we're going backwards" with the issue.
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.
Moise Kean, Blaise Matuidi and Sulley Muntari have all suffered similar abuse when playing against the Sardinian club.
Cagliari escaped punishment following the abuse to Kean after the Italian Football Federation ruled the chants had "limited relevance and perception".
"Many players in the last month have suffered from racial abuse. I did yesterday too," Lukaku said in an Instagram post on Monday.
"Football is a game to be enjoyed by everyone and we shouldn't accept any form of discrimination that will put our game in shame.
"I hope the football federations all over the world react strongly on all cases of discrimination!
"Social media platforms (Instagram, Twitter, Facebook) need to work better as well with football clubs because every day you see at least a racist comment under a post of a person of colour.
"We've been saying it for years and still no action.
"Ladies and gentlemen it's 2019. Instead of going forward we're going backwards and I think as players we need [to] unify and make a statement on this matter to keep this game clean and enjoyable for everyone."
Cagliari vowed to identify and ban the "ignorant" individuals guilty of "shameful actions".
"Full solidarity to Romelu Lukaku and even stronger commitment toward annihilating one of the worst plagues that affects football and our world in general," Cagliari said in response to the racist chanting.
"Cagliari Football is asking everyone to help you win a battle that involves everyone. No one excluded."
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."
On Saturday, Kurt Zouma became the latest Premier League or EFL footballer to suffer racist abuse on Twitter following his own goal in the 2-2 draw against Sheffield United.
Serie A response
Serie A have condemned the incident at the Sardegna Arena placing on record their opposition to "all forms of discrimination".
"Gaetano Micciche and Luigi De Siervo, President and managing director of Serie A, would like to place on record a firm condemnation by Serie A in relation to the episode of racism which involved Inter Milan player Romelu Lukaku.
"Serie A has always sided against all forms of discrimination and is strongly committed to countering a hateful phenomenon which - although perpetrated by a few stupid people - damages the whole system.
"In October we will launch a nation-wide and international initiative involving the 20 Serie A teams aiming to raise awareness among all supporters on such a delicate and important issue.
"We will ask each club to put forward a player who will become part of Serie A's "Team against Racism", a testimonial that will be the first-person bearer of the values of respect and equality.
"Racism is a cultural issue and we will need everyone's commitment, from staff to fans, to spread a positive, consistent and appropriate role model in a civil country such as Italy."
Twitter agreed to discuss racist abuse with football anti-discrimination group Kick It Out for the first time last month after Chelsea striker Tammy Abraham was targeted online.
Twitter told Sky Sports News: "We continue to take robust action on accounts which violate the Twitter Rules. Racist behaviour has no place on our platform, and is a complex issue.
"That's why we are committed to working with civil society stakeholders to develop solutions to this unacceptable behaviour - both online and off."