The Swans ran out 5-0 winners at Wembley, in a game they were expected to triumph.
Nathan Dyer opened the scoring for the Premier League side, before Michu added a second before half-time.
Dyer then notched his second of the day with a curling, left footed effort, before Jonathan de Guzman struck twice, the first from the penalty spot after Matt Duke was sent off, to complete the scoring.
The Dane was thrilled with the result and praised Bradford for their run to the showpiece final:
“I am very proud of my team today.” He told Sky Sports.
“To do what they have done on their way to Wembley, Bradford, they have beaten Arsenal and Aston Villa, among others. It’s not easy but after the second goal you could see the difference.
“They have never been behind against a Premier League team. We had to move the ball with good pace and score the first goal. We did that. I think we played a very good game. We were great.”
The former Real Madrid and Barcelona midfielder went on to reveal that lifting the trophy is up there as one of his best achievements in football and said that he is excited to be taking Swansea into the Europa League next season:
“As a manager, it is absolutely at the top. Winning a trophy for the first time in 100 years…
“The first trophy is always special and next year we will be in Europe, it will be a nice experience.”