The Brazilian defender raised eyebrows when he and Van Persie traded jerseys on the pitch as the teams walked off with United leading 1-0 at half-time.
Wenger revealed that he has spoken to the 29-year-old over the incident and assured Arsenal fans that he will not do something similar again.
“It’s interesting because Santos is a player who cares. If you speak with him, he gives an image of himself which is not him,” Wenger said ahead of Arsenal’s trip to Schalke on Tuesday.
“He is serious, he wants to do well. It is about the result, about the team. [Asking for a shirt at half time is] a difference of culture.
“I can understand that an English guy doesn’t understand it and I’m French and I don’t understand it either. He is completely in a different world when he does that.
“But he cares and he understands today what it means and, believe me, he will never do it again. I spoke to him about it but I do not want to make too big a story of it.
“I believe that was not the right thing to do at all, but that is not an explanation of our bad performance on Saturday.”
Santos has since apologised over the incident, telling 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.”
• The teams met in the 2001-02 group stage when the coaches were, as now, Arsène Wenger and Huub Stevens. Arsenal won 3-2 at home but lost 3-1 in Gelsenkirchen.
• Schalke have lost their last two home contests with English sides and not scored in three. They went down 2-0 to both Manchester United in the 2010-11 semi-final first leg and Manchester City in the 2008-09 Uefa Cup group stage. Their home record against English teams reads W3 D1 L2.
• Their win at Montpellier was only Arsenal’s third in 13 away matches in the competition proper, a run that includes eight defeats.
• Klaas-Jan Huntelaar and Thomas Vermaelen were team-mates at Ajax from January 2006 to January 2009.
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