Michael Tonge was on target in the 35th minute at Elland Road, while El-Hadji Diouf added a late strike before Luciano Becchio converted a stoppage-time penalty to dump out the Premier League visitors.
Manager Warnock 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.
The boss feels Leeds impressed from the opening whistle and believes his men could have won by an even greater margin against a below-par Saints side.
"Amy came tonight, she just had a word in my ear about it," said Warnock.
"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. 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 on Tuesday.
"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."