Two goals each from Robin van Persie and Danny Welbeck secured three points for the champions in David Moyes' first Premier League match since succeeding Sir Alex Ferguson
Despite having an even share of possession throughout Saturday's fixture, and more chances than their opponents, Swansea failed to significantly test United goalkeeper David de Gea, while the visitors were ruthless at the other end.
Two goals each from Robin van Persie and Danny Welbeck saw the champions start with a win, with only record signing Wilfried Bony able to find the net for Laudrup's side late on.
"Our plan was to put them under pressure," Laudrup said. "We knew it would be a long game and it worked well for the first half hour as they only had one shot on target.
"But then you see that difference – and the first goal was a great finish. But to concede two goals in two minutes against a team like Manchester United makes it very difficult after that.
"We created some chances after that but the third goal meant it was game over. The main difference was the finishing, and losing the two goals like we did was a huge blow.
"It’s always difficult to play the big teams, but I would rather play them at the start of the season. There is always that doubt, but the difference in today’s game was the finishing."
The 49-year-old, who guided Swansea to their first major trophy last season in the Capital One Cup, insisted, though, that he would move on quickly ahead of the club's UEFA Europa League play-off clash with Romanian's Petrolul Ploiesti on Thursday.
"I said to the players that we just have to move on," he added. “We are playing for different things within this league and its not against teams like Manchester Untied that we need to see where we are.