The 20-times English champions have produced encouraging displays in the States, also beating Roma and Inter Milan, as they prepare for the start of the season under the 62-year-old coach.
United have played their tour matches with three centre backs and it will probably be the former Netherlands coach's preferred formation this season.
"It's amazing that they have picked up a new system like that, because it's not new for (Juan) Mata, for example – he plays in his position. Neither for (Wayne) Rooney, (Danny) Welbeck nor the two midfielders," Van Gaal said in the post-match press conference.
"The greatest impact with this new system is on the back line. But we only conceded one chance in the first half and two in the second."
Two first-half goals from Ashley Young and an 80th minute strike from substitute Javier Hernandez ensured United's victory in front of 109,318 people, the largest crowd to watch a soccer match in the United States.
Real's only goal came in the 27th minute when Gareth Bale converted from the spot after he was fouled in the box by Michael Keane.
Manchester United celebrates a goal against Real Madrid during the Guinness International Champions Cup at Michigan Stadium.
Van Gaal said Keane and fellow defender Tyler Blackett would grow better with experience.
"You saw them play today and they can do the job but not for a lot of matches – they can do it for one match.
"Maybe when you give them more matches, their experience shall increase.
"But today the penalty was not so smart. He (Keane) has to learn from these errors.
"It's the same for Tyler – he can also play at this level but can he play match after match? That is the question and I cannot answer that at the moment."
Van Gaal said the victory will boost the confidence of the team, which finished a lowly seventh in the league last season and also missed out on qualification for the European tournaments under the then coach David Moyes.
"It's a very good result for us and it gives confidence to the players. I changed players in the second half but in spite of that, we scored again," he said.
"This wasn't a friendly - I had the feeling that Real Madrid didn't want to lose, which is why Ronaldo came on earlier than Carlo said (he would). But we won and deserved to win."
(Writing by Sudipto Ganguly; editing by Amlan Chakraborty)
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