Van Gaal was critical of Van Persie's form following United's 2-1 win over Arsenal at Emirates Stadium last month.
The 31-year-old Netherlands international has responded in the only way he knows how, with goals, scoring three in as many games.
Van Persie bagged a brace in a man-of-the-match performance against Southampton last week and Van Gaal paid tribute to the Dutch veteran ahead of Sunday's hosting of Liverpool at Old Trafford.
"I am very happy for him," said van Gaal. "He didn't play very well [for a short spell], but you have to compare him with other players at that time. He was lucky because [Radamel] Falcao was injured.
"I had to compare him with [Wayne] Rooney and [James] Wilson. With Rooney, I can play a lot of positions.
"Wilson is a young talent and he has to show himself also in the training sessions."
Van Persie has now scored six Premier League goals this season, making him United's leading goalscorer.
"I have always played with two strikers," Van Gaal explained. "And only three or four times with one striker.
"Maybe he [Robin] was lucky, but I have a lot of confidence in him. I have already explained here what I like in a striker.
"Not only [the ability to] make goals, but to also be an attacking point and to see the third man [to link with when he joins the attack]. Van Persie is one of the best strikers at that."
