The Swans' thrashing of the League Two club was the biggest winning margin ever recorded in the tournament's final, and Laudrup ranked the accomplishment as the best of his managerial career.
"As a manager it's absolutely at the top, winning a trophy for the first time [for Swansea] in 100 years," Laudrup told Sky Sports. "The first trophy is always special, and next year in Europe it will be a nice experience."
Nathan Dyer and Jonathan de Guzman scored two goals apiece, and Michu added another to ensure that Swansea did not become the latest top flight team to fall to giant-killers Bradford. Laudrup praised his side for going about the match in a professional manner and not underestimating Phil Parkinson's team.
"We knew what [Bradford] had done on their way to Wembley against Wigan, Arsenal and Aston Villa amongst others so I think it's a great performance," Laudrup said. "It's not easy, but after the second goal I think we could see the difference. I'm very proud of my team today.
"Bradford have never been behind against the big Premier League teams so we said we had to move the ball with good pace and score the first goal and we did that.
"I think we played a very good game and we moved the ball around, we did great.
"When you play 3-0 up with the confidence like that you see the difference between a Premier League side and a League Two side but again I have to say what Bradford have done this season is quite impressive."