Two second-half goals from Jonjo Shelvey and Chico Flores ensured the Swans' first win in nine Premier League games, lifting them into the top half of the table.
With just six points separating Swansea in 10th from bottom club Cardiff in 20th, Laudrup was relieved to gain a valuable three points.
"It's a massive win for us for a lot of reasons, it's been quite some time without a win," Laudrup said.
"It's always important to pick up points, but especially against direct opponents like Fulham.
"The first goal was very important and they could have had it. But once we got the first goal, we dominated the rest of the game. It could have been even more if it wasn't for some great saves."
Laudrup also revealed that striker Michu should return to the side within a fortnight, having been out of action since their 1-1 draw with Norwich on December 15.
"He's not that far away. I don't want to put any pressure on him, but I think he will be back in about 10-14 days," Laudrup said.
Whilst admitting he is waiting on a response from Tom Ince regarding a potential move to the Liberty Stadium, the Dane insisted he will not let defender Neil Taylor leave unless they can get an adequate successor in the remainder of the transfer window.
"I always understand when players, if they're not playing regular football, want to go elsewhere," he said of the Welshman, a transfer target for Fulham.
"We have two left backs and we have a lot of games to play, we're still in three competitions.
"If we cannot get a good replacement in for Neil then we cannot let him go. We would have to wait and see until the summer."