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 side 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 tonight's [Tuesday] 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 [Wednesday], but the powers that be wanted it to be tonight [Tuesday].
"But we gave the players who have not been in the team to 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.
"I have to take full responsibility. When you look at it, though, we played 48 hours ago, we use the second day as a recovery day and I didn't want to risk injury as we have a few as it is. But, when someone puts on the shirt for Southampton Football Club, you expect them to perform at the highest level."
Away from tonight's game, Adkins refused to elaborate on the situation with Poland goalkeeper Artur Boruc, with the club investigating allegations he threw a bottle at his own supporters during the Spurs game.
"There will be a full investigation. I don't know what the accusations are exactly, but we'll have an investigation and take it from there," was all he would say.
For his part, Warnock had nothing to be concerned about, on or off the field.
The veteran tactician is trying to make daughter Amy's wish to see him manage at Wembley come true and, with his side now one of three non-Premier League teams left at the last-eight stage, thoughts are starting to turn towards a possible trip to the capital.
"Amy came tonight [Tuesday], she just had a word in my ear about it," Warnock said.
"I thought that right from the off we were at it. I wanted us to enjoy it because if all the games are like our draw with Charlton last week, I would be better off fishing.
"We played some good football tonight [Tuesday]. In the second half, when it was 1-0, I said to my assistant Ronnie Jepson that extra-time would kill us, because you thought Southampton would always have that chance.
"But we didn't sit back and we should have scored more goals."
Having managed QPR as Premier League newcomers a year ago, Warnock was well aware of the selection quandary Adkins found himself in tonight [Tuesday].
He did not believe a weakened opposition had been the reason for his side's success tonight [Tuesday], though.
"I have been in Nigel's position," he added. "When you're in the Premier League, your position is far greater financially. But we can only beat the side we play against."