The Reds welcomed Premier League rivals Southampton to Anfield with a 1-0 deficit from the first-leg to overturn but found themselves unable to penetrate the Saints' rigid back-line for the third time this season.
Daniel Sturridge wasted Liverpool's best opportunity and late into stoppage time, Shane Long punished Klopp's charges on the counter-attack to book the south coast club's place in the competition's final next month with a 1-0 win on the night and a 2-0 aggregate victory.
With that goes Liverpool's best opportunity to win silverware this season and leaves them having lost more games in seven matches of 2017 than they did in 23 games across all competitions before the New Year.
Klopp: It would be really strange to start questioning ourselves now
Asked whether there are fears this result will leave any form of hangover, Klopp said: "No, absolutely not. Absolutely not. I said something like this a second ago [in a different interview], if we would doubt the way we are after these little, little problems we've had now - it would be a really strange thing."
The German said that his side are "absolutely in the situation" where they "don't have the points we want" but said "that's not the problem" and that is "how it is."
He declared Liverpool "know what we want to do" and "know what we have to do", as well as stating that they "know about the football we want to play" which is "all good."
Klopp acknowledged that "there are times" where that hasn't seemed the case and "it didn't happen" but praised his players for producing "a really good performance in difficult circumstances" in their second-leg against Southampton.
He referred back to when he first arrived at England and said he spoke "about the wind" a few times and "everybody was laughing" but vowed: "Today [it] was really, really difficult to play football with this wind. I am fine with this [performance] but disappointed about being out."
We don't have a problem with defensive teams, says Klopp
Liverpool once again faltered against a team that packed numbers behind the ball and overcrowded the final third to thwart the space available to the Reds' gifted attack.
The manager was asked about the challenge of coming up against teams who defend deep and play on the counter-attack and said in response: "For me as a coach, it's not that difficult because we have other situations. You can win the ball back an different things."
He continued to say that Liverpool are "not the only team in the world that has to do this" but said that "quite a lot" of teams playing against them are "playing like this" - insisting "70, 80 per-cent of the games are like this."
Klopp refused to be critical of such a defensive style, saying instead that they "knew it before" and so it is "not a problem" but added: "We still adapt to it, 100 per-cent. We did it. You have to score in this or that situation then the game changes a little bit. Not against each team, but a few teams are happy with only being one-nil down or whatever."
He said that they "don't have to think about this" but accepted that it is "the most difficult thing in football" to play against such well-defensively-drilled teams.
Klopp praised his team as "a good football-playing side" and said that Southampton "usually play completely differently" and that "if they always played like this, they would probably have a few points more because their counter-attacking was really good, and [they were] defending with a little bit of luck."
"Creating chances against a team like this, that's really not easy, but we did it so that's good," Klopp continued, though he admitted that "then you have to score."
He noted that it "didn't happen" for his team but said it is "not a problem in general" and more "only a problem for tonight."