Swansea will resume league business with a trip to Tottenham on Sunday, but they can head to north London elated at securing a first semi-final appearance in a major cup competition since 1964.
Laudrup said: "It's fantastic to reach a semi-final.
"I asked all the players before the game if any of them had played in a cup final, and no-one had.
"When you are three games from a final you get tense, and that is what we saw tonight.
"Everyone can be proud we are in the semi-finals, but when you are there you want to go the next step and be in the final. Whoever we play next, it will be very special."