The Gunners left the Liberty Stadium with three points thanks to second-half goals from Nacho Monreal and Gervinho but the Swansea boss was keen to praise both teams after the game.
"In the first half I think both teams played very well," Laudrup told Sky Sports.
"They had a couple of very good shots from distance with 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.
"But then the first goal obviously decided the game and it was Arsenal who scored it.
"In the second half I think we could have done more but I think neither of the teams did very much to make the goalkeepers work - maybe because both teams play very well in the midfield.
"In the end they won because they scored the first goal."