Goals from Wilfried Bony, Michu and Jonathan de Guzman allowed the Swans to record an invaluable three points away from home in what is one of the Welsh clubs best results in their history.
Laudrup admits he does not know where it ranks for the Liberty Stadium outfit but does believe it shows they are certainly capable in Europe.
"I have only been here for 15 months so others can say where this ranks in the club's history, but it is a fantastic evening and fantastic result,” he said.
"I've had some great nights as a manager, it's difficult to take in because this has only just happened.
"But I am so pleased for everybody because now they know they can play against the biggest clubs in the biggest stadiums without any problem and that's great to see.
"There were lots of our fans here. I think they had a great night, one of those to remember, this experience is great for them."