He insisted that a win in the cup final would be massive for him, as well as the club and it's supporters.
"It will be my biggest achievement as a manager," Laudrup told The Telegraph. "Because it will be a small club winning a trophy, because of what it means to the club and to the city it will be huge."
Swansea will also have to deal with the unique pressure of facing a League Two side in the final.
Laudrup continued: "It puts some pressure on us and we have to accept that we are favourites for the simple reason that we are a Premier League side.
"We have to play a League Two side and that makes this an extraordinary final. In 10 years' time people will still remember the year that Swansea played Bradford.
"We can win this game and they will still be remembered, that's the deal."
The League Cup final kicks off at 4pm this afternoon.