Goals from Michu and Jonathan De Guzman secured a 2-1 success at Newcastle, who were beaten at home for the second time in as many weeks.
Swansea won at Liverpool in the Capital One Cup, but their only previous away victory in the league was a 5-0 thrashing of QPR on the opening day.
Laudrup said: "It was the best away performance this season, including QPR and Liverpool.
"To come here and play Newcastle at a moment when we knew Newcastle really needed a win - because they think they belong much higher than they are now - we knew it would be really difficult for us.
"But we put on a great performance. We can always discuss what is a big goal chance, but without my Swansea glasses, I think I can say we created at least eight or nine quite big chances.
"That's very difficult to do as an away team against a team like Newcastle's."