"I think we deserved more," said Laudrup, whose side have now gone six Premier League matches without a win. "The first half was tight, there were not many chances but they came out second half and went in front with a strike from distance.
"We fought back as we really wanted something out of this game but the thing that is most disappointing is I thought in the last 10 minutes they were happy to take a point.
"We were still pushing to get a winner and then they got it from a free-kick.
"But we have to accept it."
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."