The south Wales club face Middlesbrough in the last eight of the Capital One Cup on Wednesday.
The 48-year-old enjoyed numerous cup successes during his glittering playing career.
The Dane won the European Cup with Barcelona at Wembley in 1992 as well as domestic knockout triumphs in Spain and Holland.
During his managerial career he has also experienced cup success in Denmark with Brondby and guided Getafe to the Copa del Rey final in 2008.
But Swansea had never previously reached this stage of the League Cup in their 100-year history, and Laudrup is aware this is a special opportunity for his squad.
"I won medals with big teams but that's different because you can go to a final and lose but the next year you get the chance to go to another final and perhaps win, or win the league," he said.
"But at a smaller clubs it's different. I can say it because I tried it with Getafe and it was a fantastic year. It was difficult because we started so poorly in the league and it nearly cost us in the end because we had three competitions and it can be difficult.
"But if we win that will be January's problem with three competitions to play for.
"But in this competition where we can go into last four which could be great, not only for the fans but the players as well.
"I don't know how many of these players have been in finals. I know Pablo (Hernandez) did with me, it is so different to play a game to win a trophy."
He added: "You go into the league and can say your target is this or that, to avoid relegation or finish in mid-table, but there is no trophy. The trophy is to play one more year.
"But to actually play for a trophy is fantastic."
But Middlesbrough, flying high in the npower Championship, stand between the Swans and the next step on the road to Wembley.
Tony Mowbray's side are focused on their promotion effort, but would relish the opportunity to repeat their League Cup triumph of 2004 and the Teesiders have shown their ability to cause an upset on the road with their win at Sunderland.
But should the last-eight clash end up going the distance, the home side will go into a penalty shootout without any rehearsal.
"I have my opinions about penalties. I don't think you can practise them," said Laudrup.
"You can practise 100 times about where you want to put them, but when you walk from the centre circle to the spot and think about what you have to do the goal gets so small, the keeper so big and you cannot practise that."
"The dual between the player and the keeper is something special, it is about your mentality, you cannot train that."