Former Manchester United player Lukaku appeared to be subjected to monkey chants as he prepared to take – and score – a match-winning penalty in Inter's 2-1 Serie A victory at the Sardegna Arena on September 1.
However, following an investigation the sporting justice panel of the Italian Football Federation (FIGC) ruled that the chants could not be considered discriminatory in terms of their "scale and realisation", so therefore had decided not to apply sanctions to Cagliari.
Anti-discrimination campaigners Kick It Out were left stunned by Tuesday's ruling.
A statement released to the PA news agency read: "This is a cowardly decision from Serie A and the Italian FA, in response to disgusting racist abuse aimed at Romelu Lukaku.
"Match officials ignored blatant monkey chants during the game, Cagliari have faced no punishment and we have no faith that Hellas Verona fans will be sanctioned for racially abusing Franck Kessie on Sunday.
"We can only assume that the Italian authorities do not care that they are effectively endorsing this behaviour, and creating a climate in which a pundit feels comfortable racially abusing Lukaku on live TV.
"As they refuse to take action against repeated racist abuse by the same group of supporters, it's about time UEFA stepped in and showed some leadership.
"The #EqualGame campaign means absolutely nothing if supporters are allowed to get away with this behaviour."
Cagliari police told FIGC investigators that "only on the occasion" of Lukaku's penalty were "chants, shouts and whistles aimed at the opposition athlete as he prepared to take his shot".
Individual spectators were observed chanting at the Belgian but, because of the volume of the noise emanating from the stand, it was not clear what was being said and so it could not be proven that it was discriminatory.
After the match, Lukaku took to social media to urge action against racism in football.