The Swans boss was anticipating a 0-0 draw at the Liberty Stadium when Nacho Monreal opened the scoring before Gervinho added a second but praised his side's first half showing
With 15 minutes remaining, the Spanish left-back beat Michel Vorm to open the scoring, before Gervinho rounded off proceedings with a second goal in injury time.
The Swans boss rued a disappointing second half and thought a game lacking in clear-cut chances would end as a goalless draw.
"I think both us and Arsenal did less well in the second half," he told Sky Sports. "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."
The Danish legend was, however, pleased with his side's first-half display and believed both sides exhibited their ability to control possession.
"In the first half I think both teams played very well," he remarked. "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."