Barry has confirmed to the FA that Costa did not sink his teeth into the midfielder’s neck during the 84th minute fracas which led to the forward being red carded for a second booking.
But Costa may face an extra one match ban for his behaviour leaving the field.
The FA are also studying footage to establish whether Costa flashed a V sign as he left the pitch. If he was found guilty that would also incur a ban.
The duo had a running battle throughout Everton’s 2-0 FA Cup quarter-final success, but tempers flared when Barry sent Costa tumbling to the ground in the closing stages.