Gianluca Scamacca struck either side of half-time before Mario Pasalic capped an impressive win for the Italians at Anfield as Liverpool slumped to their joint-heaviest home defeat in European competition.
"It just was a really bad game, oh my god. We started well, really well, and then didn't continue. I think even before they scored, we just lost the plot a little bit, we were everywhere and nowhere," Klopp told reporters.
"(The) midfield was spread like that, right midfielder left side, left midfielder, striker. I didn't recognise that, that was really strange. In football terms that's tactical discipline.
"We played a bad game, we deserved to lose and we must feel that now."
Liverpool will seek to overturn the deficit in the second leg in Italy next week, but before that they host Crystal Palace in the Premier League on Sunday.
With the Merseyside club involved in a tight title race with Arsenal and Manchester City, Klopp said the players had to move on from Thursday's defeat quickly.
"The boys have exactly this night to feel bad about it and then we have to build up again for the Crystal Palace game, that's how it is," he added.
"This was a low point for us performance-wise tonight, I would say, for a long time."
