The FA also ruled that Gabriel’s three match ban should be overturned, though the defender still faces a charge of improper conduct.
Arsene Wenger had been critical of the striker’s actions in the aftermath of the game, claiming that referees are too weak in dealing with the Spain international.
He told the BBC: “Costa twice should be sent off. He hits him in the face in purpose.
“In every game he has aggravation and he gets away with it because of the weakness of the referee. We knew before the game he is only looking at that.
It is not Costa’s first ban for violent conduct last year. The striker was handed a similar three match punishment for a stamp on Emre Can in January. This decision prompted Jose Mourinho to complain of a “campaign” against Chelsea.
Costa will miss games against Walsall, Newcastle and Southampton.
