The holders saw their defence of the trophy fizzle out at the first hurdle as they fell to a 3-1 defeat at Birmingham - a far cry from the glory of a Wembley victory over Bradford just seven months and one day ago.
The Swans had entered the competition in the third round due to their Europa League commitments, with this their third game in just six days after a memorable success at Valencia and a Barclays Premier League victory over Crystal Palace.
Laudrup made 10 changes from last weekend, with midfielder Jonjo Shelvey the only survivor, but the Dane maintained his pre-match stance that he was targeting back-to-back League Cup triumphs.
"I want to go as far as possible in all competitions," Laudrup said.
"We lost the possibility to go far in the competition.
"I have no regrets (about making 10 changes). You could say 10 changes from the last game but five of the players who played here were in the starting XI against Valencia."
A frustrated Laudrup felt his side paid the price for a host of missed chances.
It was classic game of two halves as the Swans dominated the opening period and hit the woodwork twice within a matter of seconds through Wilfried Bony and Alejandro Pozuelo while also spurning a host of openings.
Their Sky Bet Championship hosts duly appeared a different animal after the break and goals from Dan Burn, Matt Green and Tom Adeyemi sent the majority of the sparse 7,470 crowd into raptures.
Bony headed a consolation for Swansea with virtually the last touch of the game but it was already over.
"I don't think I'm wrong if I say we could have been four up at half-time," Laudrup added.
"And then with Birmingham's first chance they score, and then the other two goals I think there was a little misunderstanding at the back and in the end we lost the game.
"If you have to be positive then we create a lot of chances in every game but, yes, you have to score otherwise this can happen.
"I think in the first half Birmingham did not even have one chance, a couple of shots on target, nothing more.
"We could have scored at least four but we didn't and then it gives them the confidence and belief that they can come back into the game and they did."
It is the first time Birmingham have reached the last 16 since their own success in this competition in 2011.
And their reward for the victory was a fourth-round tie at home to another Premier League side in Stoke.
"I'm absolutely delighted," Blues boss Lee Clark said.
"I think to win a game like that against the quality of opposition we're up against is very satisfying.
"Not only are Swansea the holders but I said before the game that I felt it was the hardest tie we could have got outside the so-called top six, a club that's on the up in everything that they do.
"Even though they made changes I don't think it affects them as they've got a philosophy that runs through the club."
Clark added: "I hope the players gain confidence from the victory.
"I can see the players are gaining confidence game-by-game, there were some terrific individual performances out there."
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