Danny Welbeck netted the opener in United's clash with Real Madrid in the last 16 of the UEFA Champions League and, although Cristiano Ronaldo equalised, they were good value for the draw.
"It's a good result. There were chances for both sides and it was a great game to watch," Van Persie told Sky Sports.
"We had a couple of good chances but if you had said before the game we would draw 1-1 then most of us would have taken it."
Three of those chances fell to Van Persie after the break but he saw the first cannon off the bar, before scuffing a second shot and then seeing Diego Lopez save a third effort in stoppage time.
"I had three in the second half," he admitted. "Especially the one just after I hit the bar; that was a great chance. I should have stuck that in. I just slightly mis-hit it. It could've gone in but it didn't.
"The chance in the dying seconds, the keeper made a really good save because I was counting on that one to go in."
Asked if the result gives United the advantage, Van Persie said: "Slightly. But at this level I don't think these kinds of teams really care whether they are home or away.
"We don't really care and they don't really care. It's just half-time now and we'll be ready for the second half."