The Dane believes that the Gunners' dominant second-half display made them worthy victors in the Emirates Stadium clash.
"The first half was very even, they had a bit more of the ball but we were at the same level," Sky Sports News quotes him as saying.
"In the second half they were the better team, they deserved the win and good luck in the competition.
"They created chances and pushed us back, we defended great but we couldn't get out of there. It was nice to see Michel Vorm back at his best and we blocked a couple of big chances."
The Swansea boss went on to say that Arsenal could have won the game by a greater margin, but insisted his team were the better side when the sides met at the Liberty Stadium.
"They had one or two where you say 'How did they miss that?', and then they scored with a few minutes left," he said. "Last time it was us, this time it was them."
Jack Wilshere scored the deciding goal in the 86th minute.