But it wasn’t the 3-0 defeat to Barcelona that they were complaining about.
Instead, it was a BT Sport behind-the-scenes video of Gary Lineker and Rio Ferdinand celebrating Messi’s sublime free-kick together. which didn’t sit well with those of a red persuasion on Merseyside.
But the real question is, if we can’t celebrate Messi’s greatness, why are we football fans?
“In these moments he is unstoppable. What a strike!” Klopp enthused in his post-match press conference. “He’s a world-class player.”
Andy Robertson echoed his comments, saying: “He’s the best player in the world. The free-kick is world-class,” while Virgil van Dijk added: “I'm grateful that I'm not in Spain and I don't have to face him every season.”
During the broadcast of the game itself, Klopp himself could be seen in awe at the goal.
And in the background of Lineker and Ferdinand’s embrace, Liverpool legend – and former Barcelona man - Luis Garcia could be seen in disbelief at the strike.
Granted, Garcia’s allegiances were incredibly split by the tie, whereas Lineker’s ties lie with the Spanish giants and Ferdinand’s lie with anyone but the Reds due to his Manchester United links – as has been seen during the Premier League title race between Liverpool and Man City.
Lineker shared his thoughts of the criticism the next day, writing: “Seem to have upset a few Liverpool fans by celebrating greatness last night. Admittedly it was a bit cringe, but as a former player who loves Barcelona I make no apologies for dancing to the diminutive Dios.”
The fact that he had to apologise for, in short, "celebrating greatness" seems bizarre.
The video was off air, and thus off duty. In fact, during the game, Lineker even shared the thought that “Liverpool [had] been excellent in the second half” – before adding “but where there’s Messi there’s danger.”
The presenter is a long-time admirer of Barcelona’s star man, as we all should be.
What the Argentine did last week was sublime and, quite simply, unique. If anyone else had stood over that free-kick, it would not have been a danger. But Messi is Messi.
"It was very far out, we didn't know what he was going to do,” Ernesto Valverde said after the game.
“In the end, I don't know how he does it, but he always does.
"I'd rather not think how he does it, to be honest, but he always shows up when we need him the most, this time just when we were in situations in which we had to shake Liverpool's domination off.”
Valverde has not shied away from claims this season that Barca rely on Messi.
"Of course there is a Messi dependence, of course it exists, he is the best in the world," he admitted.
His team-mates, too, are making the most of his presence, with Malcom saying earlier this season: "Simply by exchanging passes with him, I am learning so much. I want to take advantage of this opportunity to the maximum."
In the same vein, football must learn to appreciate Messi while he is here, especially as the forward prepares to turn 32 next month.
"He is a very unique player and, when he is not playing, you notice it.”
For fans of clubs such as Liverpool, who don’t get to see the five-time Ballon d’Or winner as often, that point should be emphasised even more.
If the Messi masterclass costs the Reds’ their place in this season’s Champions League, they should not be frustrated.
Nor should they be angry when the likes of Lineker are celebrating his pure genius.
Instead, let’s enjoy Messi while we can because he won’t be here forever – and that is the only thing human about him.