The Togo forward was dismissed after hitting Potters' defender Ryan Shawcross with a flailing arm at the Britannia Stadium, and has chosen not to appeal against the decision.
Although it was the 25-year-old's first red card of the season he was handed an extra one-game ban on top of the usual three-match suspension because it is the second occasion on which he has been found guilty of violent conduct.
Early bath: Adebayor heads down the tunnel after his red card
CLICK HERE FOR THE WEEKEND PREMIER LEAGUE AND CARLING CUP TEAM NEWSAdebayor was given a three-game ban earlier in the season for a challenge of former Arsenal team-mate Robin van Persie in City's 4-2 Premier League victory over the Gunners in September.
City are also without midfielder Patrick Vieira, who is currently serving his own three-match ban for violent conduct following his kick on Glenn Whelan in last week's Premier League meeting with Stoke.
Bridge can't wait to play against Terry at Chelsea, says Man City stopper GivenStoke 3 Man City 1: Adebayor sent off as Potty Blues crash out of FA CupFA Cup could switch to midweek games in bid to add touch of glamourEXCLUSIVE: Are Mancini's days at Manchester City numbered already?Zabaleta won't let FA Cup defeat disrupt Man City's Champions League pushMANCHESTER CITY FC