England Under-21 international Grealish accepted the charge but felt the three-game ban was excessive. His claim was rejected.
An FA statement read: "Aston Villa's Jack Grealish will serve a three-match suspension with immediate effect after he committed an act of violent conduct which was not seen by the match officials but caught on video."
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Grealish became embroiled in a row with Coady in the first half of the game
It is an early blow for new boss Steve Bruce who only took charge at the club last week after Roberto Di Matteo was sacked.
After the draw with Wolves, Villa are 20th in the Championship table and one point above the relegation zone and have only won once in the league this season.
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