Luke Moore grabbed his first league goal of the season five minutes from time to give the Swans the three points.
Laudrup said: "There was a lot to be pleased about today. Firstly the win and secondly our attitude.
"I spoke in the week about the fact you sometimes see a negative reaction after a big win, but our reaction was an excellent first half where we showed lots of good touches, movement off the ball, and we created chances.
"We went in at 0-0 but we deserved so much more. After that, Newcastle came into the game and had some very good chances but, like us, they did not score when they were at their best and so that late goal decided the game.
"It shows our maturity, sometimes with smaller teams when they do well and get recognition from the media you see a reaction in the game after. You can forget every game starts 0-0.
"I expected what I saw today, but I still had to say it as when you win a cup a negative reaction is normal."