The Reds missed the chance to feature in back-to-back finals under the German, who was as animated as ever following the full-time whistle.
“They won both games, they deserved it,” Klopp told Sky Sports.
“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, a good save but a lucky save. The ref didn’t see the handball of Long and it doesn’t help in a game like this.
“We had seven good chances. You have to score, and we didn’t do so we lost. I’m fine with the performance but not the result.”
Liverpool saw two strong penalty appeals turned down before the Saints put the tie beyond all doubt late on, and Klopp was baffled that at least one spot-kick was not awarded in front of the Kop.
He added: “If we could hear a referee’s whistle it would be nice. I don’t know how many times that has happened this season.
“Against Manchester United we had a clear offside goal [Zlatan Ibrahimovic], nobody says anything. Tonight a penalty, nobody says anything.”