United needed a penalty shoot-out to prevail after a 0-0 draw but van Gaal thought the victory was merited and praised substitutes Luke Shaw and Wilfried Zaha for their displays.
"I am very pleased," said van Gaal. "I think we played by far the best match (of the tour).
"We deserved the victory I think. I am pleased, not only because of the way we kept possession, but because of the quality of the opponent.
"They had only one shot on our goal and that was given by the referee (a free-kick).
"We also created six or seven chances, so then it is seven against one."
Full-back Shaw, a £27m summer buy from Southampton, was not expected to feature but ended up coming on at half-time because Reece James picked up a knock just before kick-off.
Van Gaal was pleased with Shaw's efforts and said: "I think he did very good tonight.
"He's working very hard. He was lucky today because I was going to play our friend Reece James, but he was a little bit injured.
"And so I asked Shaw to play, in spite of a very heavy training session this morning."
Zaha made his first appearance of the tour and looked dangerous, surging into the Inter box on a pair of occasions.
"I was pleased with his performance but we have to wait and see,” said Van Gaal. “He has a lot of competition with the other strikers."
Zaha said: "I played all right, I'm happy. There's so much pressure on me. Every chance you get, you have to take. There are so many players here.
"He (van Gaal) is a good manager, he will help me discover what I can do.
"All I have done is what he has asked. I've worked hard, that's what he told me to do. It's a clean slate for me.
"Last year I made advancements in my game and I just want to play for Manchester United. Hopefully, this will be my chance."
Van Gaal confirmed that United are still in the market for a new central defender.
"I am looking at the defenders we have first," he said.
"And, when you see our three matches, we are doing well, I think. But it is right that we are looking for defenders, because a lot of defenders have gone.
"We have to replace them but I also like Michael Keane and Tyler Blackett."