Gylfi Sigurdsson, back at Swansea after signing from Tottenham Hotspur, fired in the 72nd minute winner from close range to stun the hosts who had drawn level through skipper Wayne Rooney shortly after halftime.
"Of course, it is very disappointing - for the players, fans, for me and my staff," said Van Gaal after United's first opening day home top-flight loss for 42 years.
"When you have (pre-season) preparation time and you win everything and then in your first match you lose - it cannot be worse I believe. We built up a lot of confidence and it will be smashed down because of this result," he added.
After that encouraging pre-season there was a renewed air of confidence around Old Trafford as fans looked for a winning start from Dutchman Van Gaal and his much heralded 3-5-2 formation.
But by halftime the mood had changed with United trailing and the formation abandoned after 45 minutes of slow and shapeless football.
United looked little improved on the team that finished seventh last season, although the absence of striker Robin van Persie and several others through injury clearly hampered them.
The absences meant Van Gaal handed Premier League debuts to defender Tyler Blackett and wing-back Jesse Lingard while Mexican Javier Hernandez led the line.
Van Gaal's plans then suffered an early blow when Lingard was hurt in a challenge with Ashley Williams and limped off to be replaced by midfielder Adnan Januzaj in the 24th minute.
Four minutes later a well-drilled Swansea took the lead with their first real attack when Ki Sung-yueng slotted home, finding plenty of space after good work from Sigurdsson.
Van Gaal brought on Portugal's Nani for Hernandez at the interval and asked Phil Jones and Ashley Young to play as orthodox full-backs in a 4-4-2 formation.
There was a fresh intensity and purpose to United after the break and within eight minutes they had drawn level when Rooney produced an overhead flick at the back post after Jones had headed on Juan Mata's corner.
With the surprisingly subdued Old Trafford crowd now in full voice, the stage looked set for an opening day victory but United lost their momentum as Swansea, with Jonjo Shelvey orchestrating the midfield, refused to roll over.
With 12 minutes remaining the Welsh side grabbed the winner, with Ecuadorian winger Jefferson Montero's fine cross causing too many problems for Young, allowing Sigurdsson, with plenty of time and space, to slot home.
Swansea's 35-year-old manager Garry Monk was delighted with the victory.
"I am happy with the three points, that is all I care about. Okay it is United and maybe people would be thinking about nerves but we focused on what happens on the grass - 11 v 11," he said.
"We limited United in free play, to very few chances...the players were superb," he said.