Laudrup hailed a great night for his side as they claimed the most famous win in their history with a dismantling of Valencia at the Mestalla.
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 Jonathan de Guzman's stunning free-kick completed the scoring in the second half as the Swans cruised to victory which puts them in charge of Group A.
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.
"If we don't win the next game at home we're back where we started, but we can be happy today about this great result.
"I don't know whether we are favourites, I wouldn't say so after one game. Not many expected this but it is only one result out of six."
Laudrup, who steered the Swans to Capital One Cup glory last season, added: "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.
"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."
Laudrup also expressed some sympathy for opposite number Miroslav Djukic, and admitted the decision to send Rami off was not clear-cut.
"He will feel bad, I am a coach and I understand how he feels but these things can happen at a big club and he has to stay strong," he said.
"It was difficult with the red card because Bony is going towards goal and Rami is the last man, but there is a player coming in from the side.
"I think some referees would give a red card and others not, but he brought the red card out immediately so he had no doubt."
The result piles the pressure on Djukic, although many of the complaints of the Valencia fans - some of whom left their seats for 10 minutes of the second half and then protested further outside the ground after the game - were directed as much at his players as at the Serbian himself.
He said: "We wanted to improve on our defeat at Betis, but it was very difficult with the red card after 10 minutes.
"We were anxious without the ball and we have to keep working and trying to do better.
"I am the same as the players. I am responsible for the situation, it is not just about the players. The performance was not good enough but it is the same for everyone."