Lukaku, who joined Inter in a club-record deal from Manchester United last month, appeared to be the subject of monkey chants from Cagliari supporters as he scored in the Nerazzurri's 2-1 Serie A away win on Monday (AEST).
The Belgium international later called for players to "unify" against discrimination, with Cagliari fans accused of singling out other black players in the past, notably Sulley Muntari, Blaise Matuidi and Moise Kean.
However, the Curva Nord fans at San Siro – a vocal section of the Inter support –have responded to Lukaku's comments with an open letter addressed to their club's new signing.
The supporters defended Cagliari and claimed racism is not a "real problem" in Italy.
The letter, posted on the group's Facebook page, begins: "Hi Romelu. We are writing to you on behalf of the Curva Nord; yes, the guys who welcomed you on your arrival in Milan.
"We are really sorry you thought that what happened in Cagliari was racist. You have to understand that Italy is not like many other north European countries where racism is a real problem."
The group continue, claiming such chants are common to "help our teams", adding: "We are not racist and so nor are the Cagliari fans."
Attempting to explain the abuse, the supporters suggest Lukaku was pinpointed because his talent made him a threat to Cagliari.
"Please consider this attitude of Italian fans as a form of respect for the fact they are afraid of you for the goals you might score against their teams and not because they hate you or they are racist," the Curva Nord said.
They add that claims of racism support the "repression of all football fans" by highlighting "a problem that is not really there".
England international Jadon Sancho offered Lukaku his support following the incident, saying the Inter star "handled it really well by not reacting and carrying on playing".
The issue of racism has come to the fore in English football in recent weeks, with a number of black Premier League players subjected to abuse on social media.
Paul Pogba, Marcus Rashford and Tammy Abraham were all targeted following missed penalties, while Kurt Zouma was abused after scoring an own goal.