Per Alex Richards of the Mirror, the German spent much of the second half talking to fourth official Mike Dean, and Dyche was "furious with Klopp" for attempting to influence the refereeing of the game. Klopp made it clear in his press conference that he was trying to protect his players:
"I said to the referee after the first sliding tackle [made] over six or seven yards, when he got the ball and everyone liked it: 'Please, tell them they cannot do that.' It wasn't a foul but they cannot do that. It's like bowling because then four or five times it happened. Joe is injured and probably not only a little bit.
"Aggression is a part of football but be careful. Sliding over six or seven yards: these times are over. Usually someone will not let you do that. We all want to win and you can choose different ways but someone needs to say: 'Stop doing that'. Make two more steps and then you are in a normal challenge. Don't go five yards before you see the player when the grass is wet. It's unlucky what happened to Joe, but the referees have to make sure it doesn't happen consistently. That's not how it should be."
Dyche, meanwhile, had a different take on the physicality of the game, per Richards: "It's this idea of getting back to what we're about. There were some excellent challenges. That's part of that front-foot mentality. You've got to put a marker on the game."
Burnley went 1-0 up through Jack Cork early in the second half. But goals from James Milner, Roberto Firmino and Xherdan Shaqiri ensured the Reds stayed just two points behind league leaders Manchester City.
Klopp's side face Bournemouth on Saturday, and it seems unlikely Gomez will be available, which is a big blow given the 21-year-old has been a mainstay of the Liverpool team this term.
But the Reds' problems pale in comparison to Burnley's plight.
Wednesday's defeat was the Clarets' third on the bounce, and they have not earned a victory since September.
Despite leading Burnley to a remarkable seventh-placed finish last term, there are now murmurings of discontent towards Dyche:
That is not a huge surprise given Burnley are 19th and in a relegation battle.
They are only one point from removing themselves from the relegation spots, though, and they have a winnable home clash with Brighton & Hove Albion on Saturday.