Owen, 33, appeared to thump Arsenal midfielder Arteta on the back towards the end of the game.
Referee Chris Foy saw the incident at the time but did not book the former England international, which ruled out the FA taking retrospective action.
Arteta said the pair had apologised to each other after the game and that he was keen to move on from the incident.
"There was a bit of tension," Arteta told BBC Sport.
"I said, 'Michael, I'm sorry', he did the same thing and it finished there and there are no problems now."