Laudrup praised the efforts of his team as their positive run continued, following on from the midweek win over West Brom.
"There have been three great performances, each better than the (previous) one. The team is playing with a lot of confidence," Laudrup said.
"They put us under pressure for 20 minutes in the second half and you know their players can make the difference at any moment, so you can never sit easy.
"We looked in quite good shape and were only defending deep a few times."
Despite guiding his team to a first win at Arsenal since February 1982, Laudrup insists the performance today must be kept in context.
The Dane said: "For me, it is not more special than winning at QPR, or at Newcastle, it is an away game.
"Winning at the big clubs is more for people on the outside.
"For me, every away game is so difficult and now we have already won three away, plus in the cup against Liverpool, that is great for a club like us."