Laudrup: Swansea did not deserve to lose
Seamus Coleman put the visitors ahead in the 66th minute at the Liberty Stadium, before Bryan Oviedo inadvertently deflected a Dwight Tiendalli effort into his own goal four minutes later.
A superb Ross Barkley free-kick settled the tie six minutes from time, but Laudrup felt his side's performance merited at least a share of the spoils.
"We did not deserve to lose this game, definitely," he said. "We wanted something out of this game.
"Maybe thing that disappointed me most is I got the feeling in the last 10 minutes when they made the two changes that they would settle for a draw.
"They took out two offensive players and put in two midfielders and we still wanted to try to get the winner and then they got it from a free-kick.
"I think we deserved at least a point, but we did not get it and i have to accept it even if it's not easy."
Despite the loss, Laudrup praised his players' approach to the encounter against an Everton side who have lost just once this season.
"The players did really well," he continued. "We played against one of the most in-form teams in the competition."