Chico Flores handed the Swans a first-half lead before Nathan Dyer extended the visitors advantage with 17 minutes remaining.
Substitute Luis Suárez did halve Swansea’s advantage but Jonathan De Guzman wrapped up the victory when he finished off a sweeping move to dump the eight-time winners out of the competition.
“The league is most important but a cup run is fantastic,” Laudrup told BBC Sport.
“At Getafe it was the same. They were a smaller club that just started to play the Spanish Cup and we went on and suddenly we were in the final, where we lost to Valencia.
“But to be a small club in the final, it is great. In that season at Getafe, it carried on in the Uefa Cup where we played Bayern Munich in the quarter-final.
“We also beat great teams like Benfica and Anderlecht in Europe. It was great.
“Bigger clubs are more used to making finals, it is different for smaller clubs. It is the first time this club has gone so far in this cup and it is the shortest way to play in a major final and have success.
“We all agree, and me included, that the league is always the most important because it is our daily bread. But a cup run is fantastic.”
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