Leading through Didier Drogba's header early in the second half, Chelsea F.C. never looked like surrendering the lead until Robin van Persie fired home in stoppage time after Thibaut Courtois could only parry a powerful Marouane Fellaini header.
Mourinho, at the post-match press conference, declined to comment on referee Phil Dowd's decision to send off Branislav Ivanovic for a second foul on Angel Di Maria and award the free kick that led to Manchester United F.C. equaliser.
But he made clear the result was a disappointment.
"We are not happy with a point," he said, summing up the game as "a good Manchester United but a very good Chelsea".
"My feeling is that we had a good first half and a fantastic second half," he said, praising the "evolution" of his team since last season.
Van Gaal looked the more cheerful of the two bosses, even though he said it was not Manchester United F.C.'s most impressive showing since he took charge at the start of the season.
"I said to the boys it was not our best performance and that's a pity, because at this moment you have to show yourself against the better teams," he said.
"We have created a lot of chances, much more than Chelsea."
Van Gaal blamed a "lack of communications" for the defensive lapse that allowed Drogba to soar at the near post and head home from a corner early in the second half.
The Dutchman said his players had "lost our head" for 10 or 15 minutes, during which Chelsea might have scored a second, before coming back fighting.
"Chelsea is the best club in Europe, I think, who can kill the game," he said. "Nevertheless we created one or two chances and we scored a goal."
Van Gaal was adamant that Ivanovic's red card, which led to the free kick that provided United's equaliser, was deserved.
"I have seen it on television. Ivanovic kicked him (Di Maria) twice -- not once but twice (on) the ankles. You can say maybe the first time is coincidence but the second time no," he said.
But he was also tough on his own captain Robin Van Persie, standing in for the suspended Wayne Rooney, for earning a booking with an over-exuberant goal celebration.
"You have seen he did a stupid reaction after the goal. You can be excited but you don't have to pull off your shirt because then you have a yellow card, it's not so smart," he said.
As Van Persie fired the equaliser and was buried under a scrum of delighted United players, Mourinho turned away shaking his head.
But at the final whistle he sportingly embraced Van Gaal -- and added a generous tribute later.
"They (United) have one of the best managers in the world... He's one of that group. He's a great coach, he's a great manager, I think they're in great hands," Mourinho told reporters.
"The same way I had last year to build... Louis, with time, will make a fantastic team."