Bombers pair Clarke and Sullivan Robey were found guilty of making careless contact with umpires in separate incidents during the heavy defeat to Brisbane last weekend.
Clarke challenged his charge via written submission at the tribunal on Tuesday night, but it was upheld.
It meant Essendon reached the threshold of five instances of players making contact with umpires this season, with the league handing down the $20,000 penalty on Thursday.
The sanction will not be included in the club's football department soft cap.
The AFL warned all clubs before the season, and again in May, about the sanctions for repeated incidents of careless contact with an umpire.
Gold Coast were the first club to reach the threshold and were fined $20,000 last month.
"This season we have continued to observe a high number of umpire contact incidents across the league," the AFL's football boss Greg Swann said in a statement at the time.
"Amongst these instances of umpire contact, a number have resulted in significant injuries to the affected umpires.
"This is a trend in the game which we do not want to see continue."
As with the Suns, the AFL said if more Essendon players were found guilty of careless contact with an umpire, fines will be given at the league's discretion.
Another six clubs are on the verge of receiving fines.
Brisbane, Collingwood, Fremantle, North Melbourne, Sydney and the Western Bulldogs have all had players cited four times so far this season.
