The Netherlands international found the target in the 10th minute in what was his home debut for United in the Premier League.
"I think I'll always look back on this game that we won on my home debut and in which I scored a good goal," Van Persie told MUTV on Saturday.
"It was different, of course. I came here a couple of times before but I always liked this stadium, the size of it. The pitch is big, the pitch is always nice.
"Now I'm a United player, everyone knows that and I'm looking forward to this challenge."
Van Persie thanked the Old Trafford faithful for their support and underlined the importance of the win following their 1-0 defeat at Everton on Monday.
"The fans have been brilliant today, supporting us and they gave me a very warm welcome, so I'm very pleased," he said.
"It was a bit nervy, but we held on and the main thing was that we got the points today, so that's out of the way and it was a good day in the end, a good three points."
United's next Premier League game is against Southampton away from home next Sunday.