The Brazilian left-back was team-mates with Van Persie until the striker's acrimonious departure to Old Trafford during the summer.
Santos endured a torrid time against United and also came under scrutiny for exchanging shirts with the Netherlands international at half-time of a game in which Arsenal slumped to a 2-1 defeat.
Reports suggested Santos could be dropped from Tuesday's 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," the Arsenal boss said.
"I believe that was not the right thing to do at all, but that is not an explanation for our bad performance on Saturday."