"We didn't perform anywhere near what's expected of Southampton," BBC Sport quotes Adkins as saying.
"Forty-eight hours ago we had a high-intensity game and I made the relevant changes. I take full responsibility."
"We wanted to play on Wednesday, but the powers that be wanted it to be on Tuesday. 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."
Leeds are one of three non-Premier League sides to reach the fifth round of the competition along with Middlesbrough and Bradford City.