Everton have failed in their efforts to get Diniyar Bilyaletdinov's red card against West Brom overturned.
The Toffees left the Hawthorns on Saturday fuming at the match officials, with boss David Moyes refusing to speak to the media following a 1-0 defeat.
The second-half dismissal of Russian winger Bilyaletdinov just five minutes after he entered the game as second-half substitute, for a lunging challenge on Baggies midfielder James Morrison, left the Everton coaching staff incensed.
They had hoped that the dismissal and an impending ban would be rescinded on appeal and put their case to an FA disciplinary panel on Tuesday.
Their calls have fallen on deaf ears, though, and a three-game suspension will stand.
A statement released on the Toffees' official website read: "The Blues were informed on Tuesday afternoon that referee Anthony Taylor's decision would be upheld, thus ruling Bilyaletdinov out of Sunday's Premier League finale against Chelsea, as well as the first two games of next season.
"The appeal was dismissed in spite of Morrison providing a statement in support of the Everton player."