The 48-year-old former Danish international, in his first season as Swansea manager, steered the Welsh club to a comprehensive 5-0 win over fourth-tier Bradford City which guarantees them a place in the Europa League next season.
Wembley is clearly a lucky ground for Laudrup as he won here playing for Denmark against England in 1983 and lifted the European Cup at the famous stadium with Barcelona in 1992.
"So it's third time lucky for me at Wembley," he told reporters. "But I don't think I can compare this title today with something I have done before, for the simple reason that its one thing to win when you are playing for Barcelona or Juventus, but to win it with a smaller club is absolutely fantastic.
"It is Swansea's first major trophy ever and to win it in this, the centenary season, is up there with the best things I have done because it is completely different."
Laudrup won league titles with Real Madrid, Barcelona, Ajax Amsterdam and Juventus and was voted Denmark's Best Ever Player after his career ended, but in a sense, he and his team were on a hiding to nothing against Bradford.
The lowly Bantams, a Premier League club at the turn of the millennium, became the first team from the fourth tier of English soccer to reach a final since Rochdale in 1962 and the first to play in an FA Cup or League Cup final at Wembley.
They had beaten three Premier League sides, Wigan Athletic, Arsenal and Aston Villa as well as high-flying Championship team Watford to reach the final, but they never threatened another upset.
Swansea took a grip from the kickoff and after goals from Nathan Dyer and Michu put them 2-0 up by halftime, Laudrup said he knew the game was won when Dyer added the third early in the second half. Two goals from Jonathan de Guzman completed the rout and gave Swansea a record final win.
"It is not often you can enjoy a match for maybe 40 minutes, but once we went 3-0 up, I knew it was done," he said.
"It was not easy to start with, because at 0-0 or 1-0 if you make a mistake, and they can score and be right back in it, but we played with patience and in the end it was fantastic.
"This is a very special day for Swansea. There have been others, like when they had to win their last game to stay in the League a few years ago and when they won to go up from the Championship (second tier) to the Premier League. But this is a very special day, their first major honour and a place in Europe. I am very proud."
Laudrup admitted, though, that not everything went right and the squabble between Dyer and De Guzman over who was going to take their penalty was his fault.
"We have not had a penalty all season and I forget to designate the penalty-taker before the match," he said. "That was my fault, I just forgot."
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