In their decision, the Italian league said that due to the amount of noise from the supporters' section, the chants could not be proven to be discriminatory.
As Lukaku stepped up to take a penalty in a match on September 1, Cagliari supporters directed monkey chants toward the striker.
Despite the crowd's agitations, Lukaku would convert the 72nd-minute penalty as Inter won the match 2-1 at the Sardegna Arena.
After an investigation into the incident, however, Serie A have determined that Cagliari will not face any punishment, though the club were fined €5,000 for their supporters throwing plastic bottles onto the pitch.
"The Cagliari Police have indicated that in the phase before the penalty kick, and only on that occasion, from the "Curva Nord" section, usually occupied by the home supporters, there have been chants, shouts and whistles towards Lukaku, who was preparing to take the penalty kick," a statement from Serie A read.
"From the area on the left looking towards the goal some chants were perceived by individual spectators but they were not noted by the service staff, nor from the collaborators of the federal prosecutor, as discriminatory, because of the whistles and screams mentioned above.
"The assumptions cannot be proved, in terms of size and real perception."
This is far from the first time that Cagliari fans have engaged in racist chanting towards opposing players.
Cagliari supporters targeted Juventus forward Moise Kean last season, leading Juve defender Leonardo Bonucci to controversially place some of the blame on Kean for the chants.
Before that, Juventus midfielder Blaise Matuidi claimed he was subjected to racist taunts from Cagliari fans, and former Pescara midfielder Sulley Muntari said the same thing happened to him in a 2017 match.
Lukaku is off to a strong start in Serie A, having made the £74 million ($90m) move from Manchester United in August.
The Belgium international has scored two goals in three Serie A games, with Inter having won all three of those fixtures to top the league table.