Michael Laudrup hailed Swansea City's emphatic League Cup final victory over Bradford City, which marked the Welsh club's centenary year with the first major trophy in their history, as the greatest achievement in his managerial career and "up there with the best things" he has experienced in football.

Swansea defeated Bradford City 5-0 in a one-sided final in which the League Two club were forced to play with 10 men for more than half an hour after Matt Duke, their goalkeeper, was sent off for bringing down Jonathan De Guzman in the penalty area. Phil Parkinson, Bradford's manager, criticised the referee, Kevin Friend, for failing to "use common sense and a bit of discretion" at a time when Swansea were already 3-0 up, following two goals from Nathan Dyer and another from Michu.

De Guzman scored from the spot, after refusing to hand the ball over to Dyer, who wanted to complete his hat-trick, and the Dutchman added a fifth late on to complete the rout and give Laudrup a landmark moment to celebrate in his first season in charge at Swansea. "As a manager it's absolutely at the top, winning a trophy for the first time in 100 years," Laudrup said. The first trophy is always special and now next year in Europe … it's a nice experience.

"I don't think I can compare this title, what we have achieved this season in this competition, with something I have done before for the simple reason that it's one thing to win a cup with Barcelona, Madrid or Juventus but to win it with a smaller team, like Swansea, is absolutely fantastic. It's the first major trophy ever and it's up there with the best things because it's completely different."

Swansea were in control throughout against a Bradford side who were superbly backed by their supporters but never looked like reprising their giantkilling feats earlier in the competition.

"To lift the trophy is great," Laudrup said, "but I think the way we did it, 5-0 … I don't have the numbers in possession, but I think they had the first shot on target after 85 minutes – I think that says a lot about our performance because we all know what Bradford has done this season, against Wigan, Arsenal and Aston Villa.

"What they have done this season is absolutely outstanding and I think this final this year will remain in history, a small part because of us and a large part because of Bradford."

Laudrup took the blame for the squabble between Dyer and De Guzman over who should take the penalty kick. "How many games have we played this season? This is our first penalty kick," he said. "It's my fault [what happened] because I didn't even say who was going to take a penalty if we got one because I thought we would go through the whole season without getting one."

Ashley Williams, who lifted the cup along with Garry Monk, the club captain who came on as a second-half substitute, said: "This is what we all dreamed of as little boys. It's a dream come true winning the final at Wembley.

"We had a job to do and did it brilliantly. We knew there was a danger as they have beaten Premier League teams but we had a job to do and we did it brilliantly. The boys were really professional and we carried on playing all the way."