The Blues appealed the charge, which related to the Spain forward’s tussle with Arsenal defender Laurent Koscielny in a 2-0 win over the Gunners on Saturday, but the appeal was rejected. Chelsea responded by saying they were “extremely disappointed” by the verdict.
Referee Mike Dean missed Costa putting his hands into Koscielny’s face and acknowledged on Monday that he would have sent off the Chelsea player had he seen it.
It is the second time the FA have taken retrospective action against Brazil-born 26-year-old for violent conduct this year, after he was banned for stamping on Liverpool’s Emre Can in January.
Costa will miss the Capital One Cup trip to Walsall as well as looming Premier League fixtures against Newcastle and Southampton.
FA board member Heather Rabbatts has expressed her “sadness and anger” at suggestions that club doctor Eva Carneiro has left Chelsea following her conflict with manager Jose Mourinho.
Carneiro is said to have decided against returning to work after her role was changed to preclude bench duties in the wake of criticism from Mourinho for running onto the field to treat Eden Hazard.