The home side were forced to play 80 minutes a man light 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 help of a deflection.
Michu and a wonderful Jonathan de Guzman free-kick completed the scoring in the second half as the Swans cruised to victory at a stunned Mestalla.
Laudrup said: "It was a fantastic game. 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 at home in these kind of games 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.
"I am very pleased about winning here against a big side like Valencia."
Valencia were the Group A favourites and the top seed in the tournament, but Laudrup does not believe his side are now the favourites to win the group despite their convincing win in Spain.
"It sets us up for the next five games," he said. "No-one expected us to get three points in Valencia and now we have the next two games at home.
Source: PA
Source: PA