Wenger was livid with the decision to award Watford a penalty when Richarlison went down very softly under a challenge from Hector Bellerin.
'Sky Sports' report that the Gunners boss followed Swarbrick down the tunnel after the final whistle and had words with him in the referee's changing room.
Saturday's man in the middle, however, did not include any such incident in his match report, meaning the FA will not hold an enquiry.
The news comes a day after it was confirmed that Richarlison will also not face any action from the FA for his 'dive'.