A dull first half saw both sides struggle to create opportunities, but Arsenal won the game in the space of five second-half minutes.
German Serge Gnabry opened the scoring in the 58th minute, converting an Aaron Ramsey assist, and just moments later Arsenal had doubled their lead.
Ramsey's fifth goal in his last four matches was good enough to give Arsenal the win, despite Ben Davies' late consolation strike.
And Laudrup felt his side had paid Arsenal too much respect after the break.
"I think the first 45 minutes were very tight and even. Both teams were at the same level," Laudrup said.
"(There were) very few chances, I think one each. Of course, the battle in midfield was the most important thing. (But) I wanted to keep our back four high and we did that in the first half. In the second half, we started I think maybe a little too deep for the first goal.
"When you play against players of this level and you are defending so deep, one or two quality passes and they create a chance like they did. But that can happen.
"The only thing I'm a little disappointed about is that from the first to the second goal, maybe we lost a little of our position on the pitch. I think the players wanted to go forward immediately to get the equaliser.
"You do that, you leave too much space for counter-attacks, and when they have players like (Mesut) Ozil, like (Jack) Wilshere, Ramsey, you can have problems. Suddenly you are 2-0 down and then it is difficult."
Laudrup said he was pleased with Swansea's response to going two goals behind though, as they set up an exciting finish when Davies scored with eight minutes to play.
"(After Arsenal's goals) we dominated for the rest of the game," he added.
"We did not create a lot of chances but still (there were) some half-chances and then we got to 2-1 with 10 minutes to go but it wasn't enough.
"That just shows when you do that against a top team, they punish you. We were punished today in a very small period of the game but it was enough for them to win."
