It means the striker will be suspended for the Pittodrie club's final two games of the year, against Livingston at home on Boxing Day and against Hearts at Tynecastle on Sunday.
Cosgrove was sent off for a tackle on Celtic defender Kristoffer Ajer which was deemed to be serious foul play.
Aberdeen manager Derek McInnes insisted the tackle was not worthy of a red card and claimed Celtic counterpart Neil Lennon agreed with him.
The Dons boss also accused Ajer of hoodwinking the referee.
Aberdeen's appeal was dismissed at a Scottish FA Fast Track Tribunal and the original sanction re-applied.