Michael Laudrup described Swansea City's Capital One Cup win as the greatest achievement of his career.
Nathan Dyer and Jonathan de Guzman scored twice, with Michu also on target as Swansea
"It's the most important trophy I've won," said Swansea manager Laudrup.
"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."
Laudrup, who took over at Swansea from Brendan Rodgers in June 2012, had previously won three cup competitions as manager of Brondby in his native Denmark.
His lengthy role of honour as a player includes a European Cup, five leagues titles in Spain - with Barcelona and Real Madrid - and an Italian league win with Juventus.
The comprehensive League Cup victory at Wembley gave him his third success at the home of English football, having won there as a player for Denmark in a European Championship qualifier against England in 1983 and with Barcelona in their 1992 European Cup final triumph over Sampdoria.
"As a player, I had the luck to play in the biggest teams in different countries," added the 48-year-old.
"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."
Swansea beat Liverpool and Chelsea on the way to the final, but Laudrup stressed Bradford's achievement of taking the three Premier League scalps of Wigan Athletic, Arsenal and Aston Villa deserved immense credit.
"This final and this competition this season will be remembered for what Bradford has achieved and a bit for we have done," he said.
"We can be proud of this. It was a little strange being a major favourite in the final and we had to win this.
"The players did great, played with a lot of confidence, patience. Winning was the most important thing, but the way we did it was a great performance."
Swansea's victory means they will represent England in next season's Europa League - their eighth appearance in Europe - and completes a remarkable turnaround in fortunes for a club that almost lost their Football League status 10 years ago.
A 4-2 win over Hull City on the final day of the 2002-03 season saved them from relegation to the Conference.
Leon Britton played in that match and was part of a thoroughly accomplished Swansea display that proved too good for Bradford.
"Things just keep getting better and better," said 30-year-old Britton, who has played in every professional division for Swansea.
"I know we keep harping on about it but 10 years ago we were fighting to stay in the Football League and look where we are today - in the Premier League and winning our first major honour.
"We've got to give credit to everyone at the football club. They are an example of how football clubs should be run. Great days like today is what happens if you run the club well."