The Brazilian, who has signed for Gremio on a loan deal until the end of the season, sparked outrage among Gunners supporters when he swapped shirts with former Arsenal star Van Persie at half time during the North London side's loss at Old Trafford.
"You guys have a different culture than me and it is still very hard to understand why people hold this grudge over me," Santos told the London Evening Standard.
"The relationship was very good until the incident with Van Persie. I have apologised and moved on. I have all my respect to the fans of Arsenal."
Meanwhile, Arsenal will return to the Champions League next week when they take on Bayern Munich in the first leg of the round-of-16 tie.