Mourinho's team stifled the Bundesliga side on Saturday in much the same way they had suffocated Barca in the semi-finals and Diego Milito netted two breakaway goals to seal the Italian club's first European Cup in 45 years.
"You mustn't forget that we chose a very difficult playing style," Dutchman Van Gaal told a news conference in the bowels of Real Madrid's Santiago Bernabeu stadium.
"I think that it's the most attractive for the public," he added. "But you can lose and we have to be on very good form to beat a team like Inter."
Van Gaal, 58, who worked with Mourinho at Barcelona in the late 1990s, was unable to repeat his 1995 Champions League triumph with Ajax Amsterdam but has the consolation of a domestic league and Cup double this season.
"I think that the atmosphere around Bayern Munich has been changed this season because we are playing attractive football and playing for the public," he said.
"But it needs also that we are in very good shape and today it was not the case," he added.
"We weren't on best form today, also because attacking is much harder than defending."
Van Gaal said they needed France playmaker Franck Ribery, who was suspended after being sent off in the first leg of the semi-final against Olympique Lyon as Bayern bid for a fifth European Cup.
"It's always easy to say after a defeat that Ribery was missed," he said. "But we also played without him against Lyon and I don't think it's respectful to the other players.."
"But, of course, it's right that in such a match with our style we need a creative player. And Franck is a creative player."
Asked if he would do anything differently if he could play the final again, Van Gaal replied: "No.
"It wasn't a surprise how the match panned out.
"We analyzed Inter Milan and knew they would play with this formation and we knew it would be difficult. They normally play in a very organized way."
A tough, no-nonsense figure, Van Gaal said he had shaken hands with his players after the match to show he was proud of their performance.
"I gave them my hand and for me that's a lot because we lost," he said. "But this handshake means that I am proud of this team."
