Antonio Valencia struck in the second minute of the second half and Danny Welbeck scored soon after as United secured a 2-0 win on Saturday - their first in four games.
Laudrup's side had dumped United out of the FA Cup in the third round at the same ground six days before the Premier League clash and they more then held their own in the first half on Saturday evening.
But they were caught cold by winger Valencia's goal as United moved up a gear and the Welsh club never recovered as their winless run in the Premier League was increased to six games.
Laudrup was left to rue a frustrating evening which left his side 13th in the table, just three points above the relegation zone.
He told Sky Sports: "I think we controlled very well the first half, we knew it was a Manchester United side playing after three consecutive losses that would be anxious and nervous and want to win the game.
"Then after just 90 seconds (of the second half) they score a goal and that gives them a lot of strength and belief and confidence. The second goal we could have done a bit better, but that first goal really hurt."
Jose Canas became the latest Swansea player to join the injury list when he limped off early on but Laudrup hopes their injury crisis will have eased by the time they face Tottenham next weekend.
He said: "That was number nine we lost, but Jordi Amat went up from centre-back and played a great game.
"We have eight days until the next game, but hopefully we will recover some players for the game against Tottenham."
