Both Liverpool and Spartak drew their opening game in Group E and face each other in Moscow on Tuesday, but Klopp was left bemused as reporters in Russia repeatedly failed to discuss the game.
The questions ranged from a specific query on his analysis of a goal Spartak had conceded in a previous match to whether the Liverpool boss loves his players after Mauricio Pochettino professed his adoration for Tottenham's Harry Kane.
Raising his eyebrows at the latter question, Klopp responded: "I am really impressed that we are at a Champions League press conference talking about things like this.
"I really don't understand the business anymore."
There had been confusion involving the translator throughout proceedings, spiking when Klopp eventually answered: "I love Harry, too."
He clarified: "Actually, that's not important for Russia. It's just an English thing. Pochettino loves Kane - and who do I love? That's the question. It's a waste of time."
The travelling Reds. pic.twitter.com/nbut3Tf4wp— Liverpool FC (@LFC) September 25, 2017
Klopp had at least been able to discuss the merits of facing a Spartak side who are likely to be missing star man Quincy Promes, comparing the situation to Liverpool's recent slump in the absence of Sadio Mane.
"[Promes] didn't play in the last game because he was injured, but Quincy is a very good player," he said. "He has speed, he is good in one-on-one situations.
"Of course that's a weakness for each team - it is like we played the last three games without Sadio Mane, also a very good player.
"He is not the only good player in the Spartak team, but he is a very good one. It always affects performances, but we will not win because one player is out or Spartak will not win because one player is in."