The Swans had threatened during a bright start, with Angel Rangel and Michu failing to take presentable chances, before the Gunners took a grip on the game.
Laudrup said: "I think in the first half we saw some good football from both sides.
"Our philosophies are similar and they had a couple of chances with (Alex Oxlade) Chamberlain hitting the bar, we had some good chances too.
"In the second half there was less good football. There was a lot of play in midfield but no shots on target.
"I thought it would be 0-0, but when things are like that the first goal will decide the game and that is what happened, it was a strange goal, but it was a goal and that decided the game."