The Swans netted twice late in the game to continue their fine run of form which has seen them unbeaten in five and with just one loss in their last nine games.
"We knew coming here the pressure was on Arsenal because they needed a win, so I told the boys to just go out and play their own game," said Laudrup, whose side moved up to seventh after a second win of the week.
"We had to change our tactics a bit sometimes because we had injuries to our usual wide players, and had one more man in midfield."
Laudrup added: "Arsenal still have lots of possession and move the ball around with the quality players they have, but we play in that way as well.
"You can't always win at the big teams, because they have players who only need a chance and it is a goal, which is the difference.
"However, I would not now say Arsenal have lost something, they just came up against a good team - because we are Swansea, you can't say 'well, you can't do that to Arsenal'.
"We have showed in other games already that we can play like that."
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