Costa earned a second yellow card after thrusting his head at Gareth Barry before making a biting motion toward the midfielder's neck. Both players said there was no bite.
Costa also confronted the referee and the FA has given him until Thursday to respond to the charge that his behavior after the sending off "amounted to improper conduct."
The FA has also given Costa until Wednesday to provide his observations about "an alleged gesture he made towards Everton supporters while leaving the pitch at half time."
Costa is facing having his automatic one-match ban increased.
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