The Swans had the majority of possession in the Premier League encounter at the Liberty Stadium and had only shot on goal fewer than Everton's 14.
But they were forced to taste defeat for the fourth time in their last seven outings in all competitions as Ross Barkley's 84th-minute free-kick gave the Toffees all three points.
Laudrup told Sky Sports: "We did not deserve to lose, conceding such a late goal at a moment when Everton, I think, were OK with a draw.
"They had made two substitutions, taking out two offensive players and putting in two midfielders. Barkley made a great run and they scored from the free-kick.
"It was harsh and the least we deserved was a point. That's how football is.
"Their goalkeeper made a couple of great saves. I don't want to say Everton found luck, because it was a great free-kick, but they just found the three points."
Laudrup has urged his players to shrug off the disappointment of defeat quickly, with a trip to Chelsea next up on Boxing Day before their year ends with another away game at Aston Villa on Saturday.
"Even in the first half, I think we did well," added the Dane.
"We played against one of the most in-form teams in the league. We have to move on, as the games will come now every two or three days."
Laudrup also had praise for Barkley. "He is a great talent, he is a great runner with the ball, he can play in tight areas, he is definitely a big talent.
"He already has a lot of talents for someone so young."
Laudrup confirmed Swansea are set to make a decision on whether Michu undergoes surgery on an ankle injury.
"We will know more tomorrow," he said. "He may have a chance for Boxing Day but we will see, we will have a final opinion from an expert and then decide.
"If tomorrow, the information suggests he needs an operation he will have surgery in the very near future.
"Obviously we are not happy he could be out for several weeks, but the most disappointed person is Michu.
"If it is bad news tomorrow, added to what happened to Nathan Dyer last week, we will have to think about what to do in January."