The Swans thrashed League Two outfit Bradford City 5-0 at Wembley on Sunday to win their first ever major trophy.
Laudrup, who won five La Liga titles, a Scuedetto and a Champions League trophy as a player, believes that his success with the Welsh outfit is the most impressive feat of his career.
"It's the most important trophy I've won," Laudrup told BBC Sport. "You will win trophies with big clubs. With smaller clubs it's very rare you go into finals, and when you do you normally play one of the big teams.
"As a player, I had the luck to play in the biggest teams in different countries.
"Swansea is not the biggest team in the Premier League but we are here winning a trophy and that is fantastic. To win a trophy with a smaller club is outstanding."
The 48-year-old has previously won three cup competitions while in charge of Danish club Brondby.