The Brazilian left-back endured a torrid time against United and also came under scrutiny for exchanging shirts with the Holland international at the interval of a game in which Arsenal slumped to a 2-1 defeat. Santos was team-mates with Van Persie until the striker's acrimonious departure to Old Trafford during the summer and the action angered some Gunners fans.
He told The Sun: "I'd like to apologise to supporters who felt aggrieved by it. Did I think it would cause such a commotion? Of course I didn't, otherwise I would have told Robin to exchange the shirts away from public view."
Reports suggested Santos could be dropped from the Gunners' Champions League tie at Schalke as a result but, while angry with the left-back, boss Arsene 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 manager 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."
- Sports & Recreation