Rooney netted a hat-trick as United beat Club Brugge 4-0 on the night and 7-1 on aggregate to qualify for the Champions League proper.
Those were the first goals of a difficult campaign to date for the England striker, who has come under fire for some of his early season performances, but Van Gaal says he has the right mindset to recover.
"I have given him always the confidence that a player needs, but I think Wayne has a very strong mentality and with his level he always shall come back," he told reporters. "He proved that this evening, but also there's still a long way for him and also for Manchester United."
On the performance, the United boss added: "I'm very happy. It was very important to qualify for the Champions League and we've done it.
"We need more victories like this, that's four clean sheets. And we created chances, but Brugge had to come and leave us with chances. But I was happy."
Van Gaal handed Ander Herrera a place in the starting line-up for the first time this season in Belgium, and after a slow start he set up the second of Rooney's treble and found the net himself.
"He started not so good, he had a lot of ball losses and got a yellow card so I wanted to change him. But I saw he was coming back, and he came into the game. I saw he played well in the double-6 position, but also later in 10 so I'm very happy for him."
United will be in pot two for the Champions League group stage draw on Thursday evening, but Van Gaal says he will be watching the reserves play an Ajax XI instead.
Asked how the competition has changed since he was last involved in 2011, he replied: "I don't know all the teams, but I cannot have any influence on the draw. There was also a lady who asked me what am I going to do tomorrow, I said I shall watch the second team against Ajax because that's more important for me because I can't influence the draw."