The Danish manager admitted he was relieved to see his side overcome Roberto Martinez's men to end a winless streak of five games, claiming his side fully deserved the 2-1 victory
The 48-year-old manager was glad to get back to winning ways after five games without a victory, as goals from Michu and Pablo Hernandez helped Swansea overcome Roberto Martinez's side at the Liberty Stadium.
And the Danish boss now believes his team can build on their victory, citing the domination they enjoyed as a means for climbing the Premier League table.
"You can say there is a mixture of joy and relief, we knew today was very important for us and I think if you see the game the players played with a lot of confidence and patience," he told reporters.
"You know when you really want something, in this case a win, you cannot think you can do it in 10 minutes. At this level it takes 90 or 94 minutes and that is what happened."
Laudrup was happy with his side's control in the second half, praising Swansea's strength in possession: "From the first minute of the second half we dominated completely, we did not create loads of chances but we got closer and closer and suddenly it was there.
"We knew both teams would want the ball as they are both good in possession and I think in the first half we had a little more possession and felt comfortable."
However, Laudrup admitted he did not foresee Wigan's attempted comeback - although he was braced for an uncomfortable finish after searching for a win for so long.
"There was one goal and then we got the second and at that point everyone was thinking when would the third come to seal the win.
'But it sometimes happens in football; [Wigan] got a goal back and the game changed completely and we had to suffer for the last 20 minutes.
"They had a goal disallowed which was very, very tight but to come back after some games without winning it would be too easy to win without suffering."