The Reds went into the first leg of their quarter-final at Anfield as not only favourites to win the match, but also to go on and lift the trophy in May's Dublin final.
However, they were ruthlessly put to the sword by their Serie A visitors on the night, as two goals from former West Ham United striker Gianluca Scamacca and a third from Mario Pasalic left Atalanta in complete control of the tie at the halfway stage.
The defeat was Liverpool's first at home in any competition for more than a year, ending a 33-game unbeaten streak that stretched back to Real Madrid's 5-2 Champions League triumph in February 2023.
The Merseysiders could have few complaints about the result either, with sloppy defending contributing to all three goals as Atalanta produced one of the most notable results in their entire history.
"The lads must go home and sleep badly"
Klopp offered no excuses for the nature of his side's shock defeat, admitting that Liverpool were far from their best and that Atalanta deserved to run out such comfortable winners.
The German, who will leave Liverpool at the end of this season, also acknowledged that the players could - and should - suffer in the wake of such a loss, but urged them to react to the result when they return to action at home to Crystal Palace in the Premier League on Sunday.
"Yeah unfortunately there is nothing really positive to say about the game. The start was good. Darwin Nunez had a good moment but from that moment on it became a really bad game and there is nothing positive to say," he told TNT Sports after the match.
"I didn't like our tactical positioning in possession. We gave them one situation by passing the ball there, then everyone was chasing another guy. We scored one that was offside but it was a bad game from us. Atalanta had a good game, scored three goals and deserved to win.
"I will watch this game on Monday. I know already that if we do a couple of things better, we will be better. Can we win it back? Yes, if we play good it is possible. Can we win 3-0? I have no idea. But this feels really bad and that's important. That was a bad performance and that's how it is. That's how we lost. It feels always in this moment that they are through but until we play, they are not.
"We haven't had that that often so we have to show a reaction immediately on Sunday. In this moment it must feel bad. The lads must go home and sleep badly. But we must prepare for Crystal Palace.
"A lot of performances tonight were really 'oops, wow, I didn't know they could play like that.' A lot of the players looked really alone in a lot of moments. It was really bad. We had our biggest chances in the end and didn't use them.
"I know the boys can play better football but they didn't do it tonight and we have to show a reaction on Sunday. I'm pretty sure they will do that."
Virgil van Dijk bemoans "too many individual mistakes"
All three of Atalanta's goals came as a result of inattentive Liverpool defending leaving forwards in too much space, with the usually-imperious Van Dijk by no means absolved from blame on the night.
The captain admitted that his side were made to pay for their sloppiness, but echoed Klopp's calls for a quick reaction and suggested that Liverpool would travel to Bergamo for the second leg next weekend still believing that they can turn the tie around.
"Obviously it's not great. A very, very disappointing evening. Too many individual mistakes and we got punished for it. It feels bad," he told TNT Sports.
"With the man-marking system they do, we have to do much better. When we have the ball we have to do better and be much stronger. The spaces were open and they punished us immediately.
"A very disappointing night for all of us but we can't dwell on it for too long. We need everyone to look forward to another big game. We have to switch back onto getting results.
"We were wide open. It's more that we conceded the goals because we lost the ball in difficult areas. It hurts. But it can't put us down. We have to react pretty quickly.
"It hurts of course. We haven't lost here for a long time. But we shouldn't take the credit away from them. They punished us for being sloppy in possession. We still had chances to score one or two and unfortunately we didn't.
"If you don't believe, there's no point going to Italy. We have made it very hard for ourselves going there 3-0 down. But the way to bounce back is by winning the game on the weekend. We need everyone to switch it back on. Then we can focus on putting out at least four goals over there."
Treble hopes hanging by a thread
Thursday's result leaves Liverpool's hopes of seeing Klopp off with a treble hanging by the slimmest of threads.
As three-time winners of this competition and one of the most impressive teams in Europe this season, Liverpool had been installed as favourites to lift the trophy in May, particularly after a draw which saw them avoid Bayer Leverkusen in the quarters and semi-finals.
The Europa League is also the one trophy Klopp is yet to get his hands on during his time in charge at Anfield, having previously lost in the 2016 final.
It would take another famous European comeback for Liverpool to keep those chances alive now, with the Reds needing to win by three clear goals in Bergamo next week just to force extra time.
Klopp does already have one trophy in the bag during his final season at the helm - the EFL Cup - while Liverpool are also embroiled in a captivating three-way title race at the top of the Premier League table.
Just one point separates Arsenal, Liverpool and Manchester City as things stand, so a quick response to Thursday's result could be imperative if the Reds are to stay in the hunt for at least one more trophy until the end of the campaign.