The Swans came through qualifying clashes with Malmo and Petrolul Ploiesti to book a shot at the knockout stage - starting with a trip to the 55,000-capacity Mestalla.
Valencia, twice beaten finallists in the Champions League, have ample European pedigree, but Laudrup insists his players have nothing to fear.
He said: "I already know we can beat anyone in this competition.
"We play against teams like Liverpool, Manchester City, Tottenham and Manchester United. Teams at the same level as Valencia so there is no reason why we cannot beat Valencia in a one-off game.
"If you play Valencia or Manchester United in 10 games, you know they will win more than us. But in one game, or two games in the group stage, it is possible.
"It is an away game against the favourite in the group and we can look forward to it with no pressure at all. We have nothing to lose and all to win."
The pairing will bring back memories for Valencia boss Miroslav Djukic, whose penalty miss for Deportivo La Coruna helped Laudrup's Barcelona side to the Primera Division title in 1994, but the Serbian has paid tribute to his rival's continental approach.
"Swansea are like a good Spanish team," Djukic said. "They have good touch, they play triangles and they keep possession of the ball.
"They have good players, with very fast people on the wings, and they are well structured. We expect a very difficult game against a team who can play the ball."