Martin Jol’s struggling side could have climbed above Swansea in the Premier League with a win and might have been expected to push for the points after Scott Parker's first goal for the club cancelled out Aaron Hughes' own goal.
But Jonjo Shelvey came off the bench to secure Swansea’s first win in six matches with a 20-yard strike.
Laudrup was particularly pleased that his men stayed true to their passing style under pressure as they bounced back from conceding a controversial stoppage-time equaliser against Stoke City before the international break.
"A win is always important, an away win sometimes even more, and today even more again for many reasons," he explained.
"First of all from our point (of view) after what happened in the last game when we thought we should have won, two points just flew away in the last second, we knew that Fulham would be a very difficult opponent today.
"They have 10 points last, have lost some games recently but they had the chance to beat us today.
"They could have gone above us and away from the relegation zone, so all these things together made it a very, very important game for both of us.
"Us being away obviously added a little more difficulty. Apart from the win, which of course is great, I think the performance in the last 20 minutes of the first half and all of the second half was excellent.
"To continue to maintain the style of possession, even in a moment when you could say we could go a little more direct, to get the result we kept doing what we always do. It was a great performance."
