Wilfried Bony, Michu and Jonathan de Guzman were all on target as the Swans kicked off their Europa League group stage with a 3-0 win.
Wilfried Bony scored his fourth goal in four European games to put Swansea ahead in the Group A fixture at Mestalla, just four minutes after Adil Rami had received his marching orders for hauling down the Ivorian. Michu doubled the advantage in the 58th minute, before a stunning Jonathan de Guzman free kick secured Swansea's victory.
Laudrup was impressed by the way his side controlled the match in Spain.
"It was a fantastic game,” he said. "Of course the red card was an influence, but we dominated from the first minute to the last. It could have been more than three and I’m very pleased to beat a club like Valencia. It was our fifth game in Europe, and we were facing a big team.
"But I’m just so pleased for everyone. Not just the fans, but for the players as well. It is great to see that even if we have players without international experience, then there is no problem. We had a lot of fans here and I’m sure they had a night to remember. These are great experiences, and to win the first game in the group is a fantastic start."