Belgium's Lukaku, who moved from Manchester United to Inter earlier this summer, was subjected to the chanting while taking a penalty in Inter's 2-1 victory in Cagliari.
But an open letter from the fan group 'Curva Nord,' posted on its Facebook page, claimed the Cagliari fans were showing Lukaku a form of 'respect' and that Italy doesn't have a problem with racism.
'We are really sorry you thought that what happened in Cagliari was racist,' the group said.
'You have to understand that Italy is not like many other north European countries where racism is a REAL problem. We understand that it could have seemed racist to you, but it is not like that.'
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'Form of respect'
In the wake of the abuse directed at Lukaku, the 26-year-old posted on Instagram that football was 'going backwards.'
After scoring from the penalty spot, the striker stood and stared at the fans behind the goal -- where the chants had originated from -- while teammate Milan Skriniar was seen putting his fingers to his lips to the Cagliari fans.
The 'Curva Nord' group -- which has no official affiliation with Inter -- is a vocal section of the club's hardcore support that sit in the north stand of Inter's San Siro stadium.
But according to the post on the group's page, the abuse leveled at Lukaku was merely a way of the Cagliari fans trying to put off a player they respect.
'In Italy we use some 'ways' only to 'help our teams' and to try to make our opponents nervous, not for racism but to mess them up,' the group claimed.
'We are a multi ethnic fans organization and we have always welcomed players from everywhere. However, we have always used that 'way' with other teams' players in the past and we probably will in the future.
'We are not racist and so are not the Cagliari fans.
'You have to understand that in all Italian stadiums people cheer for their teams but at the same time they use to cheer against the opponents not for racism but to 'help' their own team.
'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.'
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This is not the first time an opposition player has been subjected to racist abuse while playing at the Sardegna Arena.
Earlier this year, Everton forward Moise Kean was racially abused by Cagliari fans while playing for Juventus.
In 2018, Blaise Matuidi was subjected to monkey chants while playing at Cagliari for Juventus and two years ago, Pescara midfielder Sulley Muntari walked off the pitch after being racially abused by Cagliari fans and was banned by football authorities for his protest.
The 'Curva Nord' statement added that by speaking out against racism, Lukaku is creating a problem that is not there.
'When you declare that racism is a problem to be fought in Italy you just help the repression against all football fans including us and you contribute to create a problem that is not really there, not in the way that is perceived in other countries,' the post said.
'We are very sensitive and inclusive with all people. We guarantee you that in our organization there are many fans of different races or fans coming from other parts of Italy that also use this ways to provoke their opponents even when the have the same races or are coming from the same areas.
'Please help us to clarify what racism really is and that Italian fans are not racist.
'The fight to REAL racism has to begin in schools not in the stadiums, fans are just fans and they behave in different ways when inside the stadium as opposed to when they are in real life.
'I guarantee you that what they do or say to an opponent player of another race is not what they would ever say to someone they would meet in real life.'
'You have to understand that Italy is not like many other north European countries where racism is a REAL problem. We understand that it could have seemed racist to you, but it is not like that.' 'The fight to REAL racism has to begin in schools not in the stadiums, fans are just fans and they behave in different ways when inside the stadium as opposed to when they are in real life. 'We are really sorry you thought that what happened in Cagliari was racist,' the group said. 'When you declare that racism is a problem to be fought in Italy you just help the repression against all football fans including us and you contribute to create a problem that is not really there, not in the way that is perceived in other countries,' the post said.
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