The Swans outclassed their League Two opponents 5-0 at Wembley Stadium on Sunday to clinch the club's first major piece of silverware.
"I'm very proud. It was a great performance," Laudrup told Sky Sports News.
"After the second goal we could see the difference. I'm very proud of my team today."
Sunday's victory saw Swansea become the first Welsh side to win an English trophy since 1927.