United emerged 5-3 winners on penalties in Tuesday's International Champions Cup clash against Inter, after both teams failed to find the net in 90 minutes of regulation time in Washington DC.
The Premier League outfit had routed the Los Angeles Galaxy 7-0 and accounted for Roma 3-2 prior to their third match in the USA but Van Gaal said the performance at FedEx Field was their best under his tutelage.
"I am very pleased," the Dutchman told reporters afterwards. "I think we played by far the best match of our sequence of three.
"They only had one shot on our goal and that was given by the referee [a free-kick], but I think we also created six or seven chances, so then it is seven against one.
"I was very pleased with our ball possession; it was much better than the other matches. And I think also the positions were better covered.
"So I was tonight very pleased with the performance of my players, both in the first half and the second half."
Captain Darren Fletcher converted the match-winning penalty in the shoot-out after Marco Andreolli fired his effort off the crossbar.
Van Gaal said his squad had prepared for the likelihood of penalties following Inter's success in a shoot-out against Real on Saturday.
"We practised penalties yesterday and also the sequence," he said. "That is why De Gea was our goalkeeper in the second half, because he is the best of the four at penalties.
"Fletcher hit the post in training so it's also a little bit of luck, but we deserved the victory."
The former Netherlands coach also heaped praise on United's defence, with a back three consisting of Phil Jones, Jonny Evans and Chris Smalling keeping their second clean sheet in three games on tour.
"The first match was zero goals, the second match was a fantastic goal by Pjanic, an error from the goalkeeper and a penalty given by the referee, and today again zero goals," he added.
Van Gaal also admitted he was searching for defensive reinforcements following the departures of Nemanja Vidic, Rio Ferdinand and Patrice Evra, with Thomas Vermaelen and Mats Hummels linked.
"We are doing well but we are looking for defenders, because a lot of defenders have gone," he said.
"We have to replace them but I like also like Michael Keane and Tyler Blackett."
