Laudrup has said that expectations at the club have now grown as a result and the players cannot rest on their laurels.
"Of course a club like Swansea can't expect to win a trophy every two, four or six years," he told The Mirror. "I read that Arsenal haven't won a trophy in eight years. David Moyes at Everton - top 10 for how long and they haven't won a trophy.
"I've already told the players, board, the chairman you can't come back after the vacation, after winning a trophy, and say only avoiding relegation is important. When people get a taste of success they like it.
"They don't want to go back. That is very difficult. That is the downside of success."
Swansea currently sit ninth in the Premier League.