"I guess it was my first touch," Van Persie told Sky Sports.
"I was a bit surprised as well, but it was a really good pass from Gervinho, I took a good touch with my left foot and it went in.
"But I didn't know it was such a quick goal. How long was it?"
The Dutchman then fired in a fine free-kick with eight minutes left to put the Gunners back in front after Sunderland had levelled before the break.
"I felt confident because it's my favourite position, but I have to be a bit critical and look at myself because I have missed many chances, so it was about time to be honest."
There was a nervy finish as Arsenal clung on for a vital three points.
"We've been there before in the last couple of minutes trying to hold on to a 2-1 score and we did well," he said.
"They pump in every single ball and they can cause problems, but we have to handle them and all of the back four defenders and the midfielders try to help each other, so credit goes to the whole team."
Before the match, Van Persie had used his programme notes to dismiss speculation about his future at the club.
"I had seen loads of comments about a story like that, I thought after one or two days it would go away, but it didn't so I felt it was time to explain things and I did that.
"I'm committed. This is my eighth year. If you can say of one player that he's committed, it's me."