Januzaj thinks United are better-equipped to recover from a setback now than they were under David Moyes, the man who led United to victory over Swansea this time last year but ended the year in seventh.
"A lot of things have changed," Januzaj said when asked about Van Gaal’s impact at the club.
"He is a top, top manager and we respect him a lot. We are working hard for him, the team and everyone else at the club.
"He was honest with us after the match but it’s only the first game."
Those United fans worried about the state of their defence were given further cause for concern on Saturday.
There was a lack of cohesion and focus from the back five, which turned into a back four after the break as Van Gaal ditched his 5-3-2 system.
United’s vice-captain Darren Fletcher was unhappy both goalscorers were unmarked when they beat David De Gea.
"We conceded bad goals," Fletcher said. "For me it felt like Swansea scored with their first attack.
"We started the second half very well and got back into the game and then they sucker-punched us again.
"It felt like they had only two chances in the game and they’ve managed to score them both. That’s hard to take and disappointing."
Sigurdsson, meanwhile, could not think of a better place to score on his second debut for Swansea.
"Getting three points at Old Trafford is always special, but to score the winner here has been a dream for me ever since I was young," said Sigurdsson, who returned to Swansea this summer following a two-year spell at Tottenham.