Goals from Michael Tonge and El-Hadji Diouf and a Luciano Becchio penalty helped the Championship side to their second successive top-flight scalp, with their 3-0 victory earning them a first quarter-final berth since 1996.
Neil Warnock's men had the run of the park against a below-par Saints side, with Adkins' much-changed line-up unable to find sanctuary from their dismal Premier League form.
But having lost to Tottenham just over 48 hours ago, Adkins was of the opinion that he could not have put his first-team players through another tough workout and accepted the responsibility for the collapse.
"We didn't perform anywhere near what's expected of a Southampton Football Club team," he said.
"Forty-eight hours ago we had a high-intensity game and I made the relevant changes. I take full responsibility. We wanted to play tomorrow, but the powers that be wanted it to be tonight.
"But we gave the players who have not been in the team the chance to show what they could do, and they did not take it."
The players Adkins refers to are the likes of veteran goalkeeper Kelvin Davis, defender Jos Hooiveld, midfielder Richard Chaplow and forward Guly Do Prado.
None of them were able to have an impact on the game, though, with only debutant substitute Lloyd Isgrove emerging with any real credit.
"It will be good experience for the young players," Adkins added. "We have tried to blood them in the past and utilised them in the cup competitions but tonight, on the whole, we haven't performed."