Shane Long scored in stoppage time at Anfield to put the South Coast club into the final, 2-0 on aggregate.
Klopp though was far from happy with the decisions taken by the referee in charge, saying the official missed a clear handball.
“I don’t look for excuses, but it’s really hard to accept [bad decisions] week by week by week. The handball was 100 percent,” Klopp said.
Report: Saints knock Liverpool out to reach EFL Cup final
“The ref did not see the handball of [Southampton player Shane] Long and it does not help in a game like this,” Klopp said.
“If we could hear a referee’s whistle it would be nice. I do not know how many times that has happened this season.”
“I’m disappointed. First half, the wind was difficult to handle. Second half we did much better, created outstanding chances,” Klopp said.
“We did really well, we cannot create more chances than we did in the second half, we were dominant. It is difficult because you have to take risks, but too many risks plays to their strengths.”
“We had big chances and no luck. A lucky save [from Southampton goalkeeper Fraser Forster], a good save, but a lucky save.”
“We had seven good chances. You have to score and we did not do, so we lost. I am fine with the performance, but not the result.”
Liverpool’s next outing is against Wolverhampton Wanderers in the FA Cup fourth round on Saturday, while Southampton earned a trip to Wembley to face either Manchester United or Hull City on February 27.