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.
Source: PA
Source: PA