Liverpool lost out 1-0 to Saints at St Mary’s in Wednesday night’s semi-final first leg, with Nathan Redmond coolly striking the winner.
Redmond missed a host of chances that could have buried the Reds, however, leaving Klopp insisting his side can produce a dramatic rescue act in the return leg on January 25.
“We will strike back, we will be a different team, different side—everything will be different at Anfield,” he said.
“So for us it’s still possible to go to Wembley and that’s the target. That’s the only comfort to take.
“Losing 1-0 is the third-best result you can get. I don’t like it too much, but it’s still possible.
“The performance doesn’t feel too good, that’s how it is. But for the final everything is open.
“At this moment there’s two disappointed managers after the game, one because he lost, the other because he won 1-0 and has to go to Anfield, and that’s how it is.”
Daniel Sturridge appeared nonplussed by a change of tactics in the second half, with other Liverpool players also bemused by Klopp’s switch.
The former Borussia Dortmund manager revealed he had altered Liverpool’s tactics to 3-5-2 and admitted failing to get the message across to his players quickly enough.
Liverpool now take on Manchester United at Old Trafford in Sunday’s Premier League encounter, with Klopp demanding an immediate upswing in performance from his side.
“It was just a new system, however you want to call it, 3-5-2,” said Klopp.
“Two wingers, two strikers, that’s all. No more information, but it was enough.
“I think we were a little bit too late when we gave him the paper when the game was already running on. That was our mistake. Things like this happen.”
Southampton boss Claude Puel admitted his side should probably have secured a greater winning margin – but insisted the Saints can still progress to the final.
“It’s a little frustration that this win was just 1-0,” said Puel.
“With just a little more luck we could have been further ahead.
“But I think it was important to keep this result with a clean sheet, with a win, and to sustain our chances of qualifying for the final.
“It was a great performance here and I believe they had just one chance in the whole game, so it’s a good performance from my players.”