Van Persie also scored the Netherlands' crucial equalising goal after they fell behind in the second half of the clash to a penalty from Mile Jedinak.
"That was the goal that got us back into the game. It was important. I knew we had to get one and preferably as quickly as possible - especially from my point of view," Van Persie told reporters.
"I wanted it extra badly because I knew I wouldn't be in the team for the next match. I'm annoyed about that."
Van Gaal's side can top Group B with a draw against Chile on Monday.