The racist chants were heard when the Belgian stepped up to take a penalty during Inter's 2-1 victory on Sept. 1.
Serie A's disciplinary panel ruled the nature of the chants were not deemed offensive in terms "size and real perception," as translated by Will Griffee of the Daily Mail.
Instead, Cagliari received a €5,000 fine after supporters threw plastic bottles on the pitch.
It's the third time over the last two years that Cagliari have escaped punishment relating to racist abuse of players. The club's supporters previously aimed similar discriminatory chants at Moise Kean and Blaise Matuidi.
Verona rejected claims that their fans were racially abusing Kessie, explaining, according to the Associated Press, that the chants were being misconceived as whistles from the stands were aimed at match officials.