However, the French boss says he does not want to see the incident, which occurred during Saturday's 2-1 defeat at Old Trafford, blown out of proportion.
The Brazilian left-back counted Van Persie as a Gunners team-mate until the striker's acrimonious departure to United during the summer.
Santos endured a torrid time against the Red Devils and came under scrutiny for exchanging shirts with the Holland international at the break.
Reports suggested Santos could be dropped from Tuesday night's UEFA Champions League tie at Schalke as a result but, while angry with the left-back, Wenger was keen to downplay the incident.
"I spoke about that but I don't want to make too much of a big story of that," said the Arsenal boss.
"I believe that was not the right thing to do at all, but that is not an explanation for our bad performance on Saturday."