The Welsh club claimed their most famous victory after the home side were forced to play 80 minutes with a man down after defender Adil Rami saw red for hauling down Wilfried Bony.
The striker went on to give Swansea the lead in the 14th minute with his fifth goal in eight games, firing home with the aid of a deflection.
A strike from Michu and a wonderful Jonathan de Guzman free-kick completed the scoring in the second half as the Swans cruised to the three points at a stunned Mestalla.
Laudrup has been keen not to state his expectations of how far Swansea can go in the tournament, but the manner of their performance against the top seeds suggests a run to the knockout stages could be in the offing.
But the Dane does not believe one result has changed his side's standing in the group.
"This result sets us up for the next five group games," he said.
"No-one expected us to get three points in Valencia and now we have the next two games at home.
"If we don't win the next game at home we are back where we started, but we can be happy about this great result.
"I don't know whether we are now favourites, I wouldn't say so after one game. Not many people expected this but it is only one result out of six.
"But I am so pleased for everybody because now they know they can play against the biggest clubs in the biggest stadiums without any problems and that is great to see."
Valencia are undeniably on a poor run of form, and their manager Miroslav Djukic is already coming under pressure despite having only taken charge in June.
A section of supporters vacated their seats for the first 10 minutes of the second half and protested further after the game.
But it should not detract from a superb Swansea performance which, understandably, left Laudrup delighted.
"It was a fantastic game," he said. "Of course a red card early in the game has an influence, but in my many years in football I have seen sides go down to 10 in games like this and still win.
"But we dominated the game from the first minute to the last minute.
"We scored three goals, and before the second we had two or three huge chances to score and it could have been even more."