The 29-year-old scored inside three minutes in a 2-1 victory over the Gunners at Old Trafford in November after completing a £24m switch to the Red Devils from the north London side last summer.
And the Netherlands international said that scoring against his former club felt strange after spending eight years at Arsenal and captaining the club in his final season.
“It was a weird day. I should’ve scored two. I’d never played against a former team so scoring was strange. But you have a job to do,” Van Persie told United’s website.
Van Persie made an instant impact for his new club as the Red Devils striker scored 26 goals in United’s Premier League title-winning campaign.
The Dutch forward’s best strike was arguably his stunning volley against Aston Villa in May, with Van Persie scoring a further two goals to seal a 20th top-flight title.
“It was instinct. I looked up and thought: ‘This ball is so nice. It’s too beautiful to take a touch’. Everything was exactly as I wanted it to be,” he added.
It was Van Persie’s first title success since moving to England in 2004, and the United striker dedicated the triumph to the club’s supporters.
“This [the title] is for the fans, players and staff. What I really like is it’s made so many people happy. Kids, babies, women, men – they’re all so happy.”