The Swans reached the Capital One Cup final, where they will face League Two Bradford, after a goalless draw in the second leg of their semi-final against Chelsea sealed a 2-0 aggregate win.
While Eden Hazard's sending off for kicking a ball boy has grabbed most of the headlines, it should not detract from Swansea's achievement.
Just 10 years ago the club sat rock bottom of the Football League, and a year earlier had faced going out of business.
That they are now managed by one of the finest European players of the last 30 years and occupy the lofty heights of the top half of the Premier League table seems barely credible.
Yet they will go to Wembley with a chance to secure their first major trophy, and the additional prize of European qualification.
Laudrup admits the six-day turnaround before travelling to face Sunderland has come at the right time to allow the scale of Swansea's success to sink in.
The Dane said: "I think everybody, the players, the staff, and the fans need a couple of days to understand we are there, but the good thing is we have a month to be ready.
"We have three games in the league before then, but we just need to enjoy it as it is not often in football you can enjoy.
"We can now enjoy this final for at least a month and hopefully for a while after."
Laudrup revealed he has already started assessing the Bantams, and paid a warm tribute to Phil Parkinson's side.
"The DVD has been invented so I have already seen four or five games.
"I have seen the games against Wigan, Arsenal and both against Aston Villa and looking at those will be important for us.
"What we have done is a small fairytale, but what Bradford have done is amazing.
"It is great what they have achieved in beating three Premier League sides, but hopefully it stops there."
While Swansea can reflect on a Wembley final, Chelsea saw another trophy slip through their fingers.
The Blues have already missed out on five pieces of silverware, with the Community Shield, UEFA Super Cup, World Club Championship and Champions League added to their League Cup exit.
Rafael Benitez's side also trail Premier League leaders Manchester United by 11 points and goalkeeper Petr Cech knows they need to discover some consistency.
He said: "We want to do better than this, that's clear.
"We had a good start to the season but then there was the Super Cup where we didn't turn up, which was a huge surprise, and then everything was going downhill.
"It ended up with a change of manager and then we picked up again. It looked like we were back on course but we have had another blip. It's clear we need to be more consistent.
"We dropped points in the league where nobody expected it and this has been frustrating because in big games we seem to do well.
"But we are still in the FA Cup, the Premier League and the Europa League. Nothing is finished yet. These are trophies that we can still win."