Laudrup admitted that he thought the match would end goalless until Arsenal finally broke the deadlock with 15 minutes to play.
"In the first half I think both teams played very well," Laudrup told Sky Sports News. "They had a couple of very good shots from distance with [Alex] Oxlade-Chamberlain, I think, having both of them.
"We also had a couple of very good chances. It was good football with two teams who like to play the possession game doing it very well.
"Then I think both us and Arsenal did less well in the second half. There were no shots on target so I thought at that stage it would be a 0-0 game. However, then the first goal obviously decided the game and it was Arsenal who scored it."
Swansea stay ninth after the result but are now four points away from eighth-placed West Bromwich Albion.