Luke Moore came off the bench to score the decisive goal in the 85th minute as the game looked to be heading for a draw.
Laudrup told the club's official website: "There was a lot to be pleased about today. Sometimes you can have a negative reaction, but I thought we were excellent today. It has been a great week for us.
"In the second half they came into the game and put us under pressure with two or three very good chances. But they didn't score when they were at their best and the late goal ended up deciding the game."
Swansea are now eighth in the Premier League following their win over the Magpies.