An Ashley Young double, followed by a goal from substitute Javier 'Chicharito' Hernandez, kept the Red Devils' undefeated pre-season record intact in front of 109,318 fans at Michigan Stadium.
Van Gaal believes the latest victory will serve as a major confidence boost for his players and says he is proud of the way the team has adapted so quickly to playing with a back three.
"Within two weeks we have played for more than 300,000 fans and that is amazing," he told reporters following the win. "We also had the chance to meet the American fans of ours which was very good as well.
"I also think the match was not a friendly. I had the feeling that Real Madrid did not want to lose and that is why [Ancelotti] went with Ronaldo earlier than he said he would. Nevertheless, we have won and I think we deserved to win.
"I think our defensive line is amazing with how they picked up a new system just like that. The greatest change with this new system is with the back line and it is amazing how they have performed. We gave away just one chance in the first half and two chances in the second.
"It's still preparation time, and the same goes for them. You saw Ronaldo come on late and we are also missing players like [Marouane] Fellaini, [Adnan] Januzaj and [Robin] Van Persie. You can't say we will beat every team now because it is not like that.
"Of course it is a very good result for us and it will give confidence to all the players. I changed a lot of players and we still scored in the second half, so we are heading in the right direction."
Danny Welbeck was forced off during the first half of the clash and Van Gaal says the player will need further tests to determine the extent of the damage.
"He had minor problems [with his knee] before the match but he said he could play. In the match he was feeling it again so we have to wait and see tomorrow what his reaction is and we will know more, but until then I can not say."
United club will now face bitter rivals Liverpool in the final on Tuesday with a chance for the team to win a trophy before the season kicks off.
"I think it's good for English football and I think that is very important that two teams from the Premier League will play in the final. It is still preseason for them so it doesn’t mean anything, but it is better to win than to lose."
United will not compete in Europe this season after their dismal Premier League campaign under David Moyes last term and Van Gaal admits it is frustrating he will not be able to face top teams from the continent in competitive games.
"There are always two sides to the coin. It is positive because I can train more with my players and I need the time. But on the other side you need also good opponents and in the Champions League you have higher level teams, so it is also a pity."
Manchester United are set to take on Liverpool in the final on Tuesday in Miami.