Lukaku was subjected to monkey chants as he prepared to take a penalty in the Serie A meeting between the sides earlier this month.
Cagliari subsequently vowed to ban the supporters responsible but rejected "silly stereotypes" about the behaviour of their fans, while Lukaku called on football authorities and players to "unify" in the fight against racism.
The FIGC said it would investigate the incident but on Tuesday its Giudice Sportivo panel ruled Cagliari would not be punished over the abuse aimed at the Belgium international.
"The head of the public order stated that police of Cagliari had spotted that in the phases preceding the penalty kick, and only on that occasion, from the sector "Curva Nord", usually occupied by the home supporters, there were chants, shouts and arguments against the athlete Lukaku, who was preparing for the penalty," said a statement.
BREAKING: Serie A have confirmed once again that Cagliari will not face punishment for the racist chanting aimed at Inter's Romelu Lukaku pic.twitter.com/pgzv6ltbsb— Andrew Cesare (@AndrewCesare) September 17, 2019
But it was concluded the club would not be punished due to the "size" of the chanting and the perception that there was too much shouting and whistling to identify its "discriminatory" nature.
Cagliari, however, were fined €5,000 after fans launched plastic bottles on to the pitch against Inter.
The abuse aimed at Lukaku is the fourth high-profile occasion Cagliari have been involved in such incidents in just over two years.
In May 2017, Pescara's Sulley Muntari was booked for complaining to the referee about racism and was later given a one-match ban for walking off the pitch, while Juventus midfielder Blaise Matuidi claimed in January 2018 he was abused.
Last season Matuidi's then club-mate Moise Kean was targeted with the Sardinia club escaping punishment as Serie A felt the chants "had an objectively limited relevance to race".
He told Corriere dello Sport: "I have been in the world of football for 40 years and have never received a suspension for behaviour in any of the roles I have held, but I accept the decision made against me.
"I would not like to pass for a racist. My partner who has lived with me for 17 years is black, I have two black grand-daughters. I am not a racist and I believe I am an educated person in every respect.
"In my career I met so many black players and I never had any problems."