The Manchester United striker salvaged a point for Oranje with an injury-time penalty, but team-mates Arjen Robben and Kevin Strootman were frustrated with the result
Van Persie converted a spot-kick after being tugged back in the area in the final minute of injury time of the World Cup qualifier which saw Louis van Gaal's side lose their perfect record in Group D.
The Manchester United star admits it was a "bizarre" match to be involved in.
"Who would have expected this?" he told SBS. "This is what's so good about football. It's unfortunate that we didn't win, but that's all part of it.
"We knew that this week would be difficult. Everyone thought this would be easy, but these youngsters are very fit. The boy who scored two [Konstantin Vassiljev] is very good.
"It was a bizarre game. We must be glad that we equalised. With a little luck, we could even have made it 3-2."
Arjen Robben was far less enthusiastic about his opponents' display and was instead furious at his own side's lacklustre performance.
"When you know you're better and you owe it to your fans to win here, it can be very frustrating to experience an evening like this," said the Bayern Munich man.
"We had to score two, three or four, just in the first 20 minutes. That didn't happen, but what happened afterwards shouldn't have done either."
Roma midfielder Kevin Strootman believes Oranje would have seen out the result had they been able to maintain their strong start, with Robben handing them the lead after just two minutes.
"We gave the goals away very easily," he said to NUSport.
"After the break we went along with their game. It's a shame we could not find a sequel to out good start."
Despite Friday's disappointment a win for Netherlands against Andorra next week would guarantee their place at World Cup 2014.