Van Gaal claimed his biggest scalp as United boss by beating the European champions 3-1 thanks to a double from Ashley Young and another goal from substitute Javier Hernandez.
The win, which came in front of a US-record crowd of 109,318, sent Van Gaal's team through to the International Champions Cup final in Miami.
There, on Monday, Van Gaal will get his first taste of United's bitter rivalry with Liverpool and he wants to see another win from his team.
"It will be another preparation game for us but it's better to win than lose," the United manager said.
"It's good for English football - I think it's very important that two teams from the Premier League shall play in the final."
United's performance at the Michigan Stadium, on the outskirts of Detroit, was the best of their four-match tour.
Not even the introduction of former United star Cristiano Ronaldo could help Real, who only found the net through Gareth Bale's penalty.
Darren Fletcher, who captained the team for the third time, successfully marshalled the midfield, negating the threat posed by Luka Modric, Isco and Xabi Alonso.
And up front, the attacking trio of Juan Mata, Wayne Rooney and Danny Welbeck threatened throughout.
The best moment of the match came when Young converted a flowing passing move that involved Welbeck and Rooney, who backheeled the ball to Fletcher on the edge of the box.
"You would come to the stadium just for that goal," Van Gaal said of United's first.
"It's a very good result for us and it gives confidence to all the players.
"The game was not a friendly; I had the feeling that Real didn't want to lose, which is why (Real boss Carlo Ancelotti) started with Ronaldo a little bit earlier than (expected).
"We deserved to win
We are in the right way and we're missing players like (Marouane) Fellaini, (Adnan) Januzaj and (Robin) van Persie."
Despite the impressive first goal, Van Gaal was happier with the performance of his defence than his attack.
The Dutchman has been pleased by the way his defenders have adapted to playing 3-4-1-2.
"It's amazing that you can pick up a new system like that," said Van Gaal, who played the same formation in the World Cup with Holland.
"It's not a new system for Mata, Rooney or Welbeck, who play in their position, neither is it a new system for the two midfielders.
"The greatest impact with this new system is on the back line.
"It's amazing we had one chance against us in the first half, and two in the second."
The only problem Van Gaal had with his back line was with Michael Keane, who left the referee with no option but to award Real a penalty after he clambered all over Bale's back in the box.
"That was not so smart
He has to learn from these errors," Van Gaal said of the 21-year-old.
Van Gaal only gave lukewarm praise to Hernandez despite his first tour goal.
The United boss, who refused to say whether Hernandez would remain at United, claimed the Mexican was too selfish with the ball at times.
"He scored a wonderful goal, prepared by Shinji Kagawa and also Fletcher," Van Gaal said.
"But after that he had to give the ball to (Tom) Cleverley, a backpass, and he gave it to Kagawa.
"I think at that time he wanted to thank Kagawa for the nice pass (for the goal), but at that time he needed to think about the team - it was better to play the backpass and Cleverley was inside near the goal, it was better."
Ancelotti, meanwhile, explained why he only brought Ronaldo on half-way through the second period.
He said: "Cristiano really wants to play in the Super Cup and for this reason I only gave him 20 minutes."
Source : PA
Source: PA