Ki Sung-yueng stunned the expectant United fans by handing the visitors a first-half lead, before newly-appointed captain Wayne Rooney scooped an overhead kick home from close range to level the scores after the break.
But just when United were expected to go on and secure the victory Gylfi Sigurdsson bundled the past David de Gea, who should have done better, to get Van Gaal's reign off to a losing start.
"We didn't reach the level we have shown in the past matches and that is disappointing because this is the most important match," Van Gaal told BT Sport 1.
"We were disappointing in defence and we are disappointed with ourselves and that's why we lost today."
The Dutch boss, who has won league titles with every club side he has managed so far in his career, quickly batted away suggestions that the opening-day performance will have a big impact on his transfer plans.
"No, because that is a short term assault I think, but of course we need defenders but I have already said that in former press conferences," he added.
"You cannot say because of one game that we lost, and all the others we won, that it is the defence. It's the team.
"We never played as a team I think and that's our error and also we don't reach the required level and maybe because of that we haven't played like a team."
Garry Monk's Swansea side took advantage of United's unfamiliarity with playing three at the back in the first half, but once they added an extra body in defence the home side looked more comfortable.
Van Gaal revealed that he decided early on in the clash to make that tactical switch to combat what the Swans were doing.
"They made the pitch very big and then we have to press more in front and the system 4-3-3 is a better system to press the ball," he said.
"We started to do that very well and we scored a fantastic goal and then we have chances to make it 2-1 but chances is not enough, you have to take the chances. The result is what counts."
In a strange twist David Moyes' short spell in charge at United also got under way against the same opponents this time last year. On that occasion the Red Devils left the Liberty Stadium with three points after a convincing 4-1 victory.
Earlier this week Van Gaal stressed that he wanted to get a victory to breathe confidence into Old Trafford again, but the memory of how last season descended into a seventh-placed finish should act as a cautionary tale for judging this opening-day result too harshly.
The 63-year-old says he now needs to go away and analyse the defeat because he cannot fault the effort put in by his players.
"The first thing that I say is that we are not reaching our level and we have to evaluate why because they have done their utmost best," he added.
"I cannot say they didn't do their best because you can see in the second half they have run all the miles together but I think we have to always keep our heads up and use the second step in our process better than we have today."