Jurgen Klopp felt referee Stuart Attwell failing to control Burnley's physical approach contributed to an injury for Liverpool defender Joe Gomez.
The England international was taken off on a stretcher in the 23rd minute at Turf Moor after a heavy challenge from Burnley captain Ben Mee sent Gomez sliding into an advertising board.
Liverpool came from behind to win 3-1, setting a club record for most points 15 games into a league season, thanks to goals from James Milner, Roberto Firmino and Xherdan Shaqiri.
But Klopp was unhappy with the way Attwell refereed Wednesday's intense clash at a rainy Turf Moor.
"The challenges from the beginning on the wet ground, the referee should have said something earlier," Klopp told BBC Sport. "I told him if you don't say 'be careful' they will keep going until something happens.
"The injury threat is hard, the first few challenges everyone likes and it is a part of football but it leads to the situation, no foul, what can I do, but Joe Gomez is injured."
At his post-match news conference, Klopp gave more details on Gomez's injury, which he fears could be serious.
He said: "I'm pretty sure I don't make a lot of friends, but that's not my job. I said after the first challenge, I don't know who did it, sliding tackle from six or seven yards, getting the ball, everybody likes it, I said to the ref 'it's no foul but please tell them you cannot do that'.
"Nobody can judge that. You get the ball, nice, but it's like bowling. Because you get the player as well. It happened four or five times, everybody likes it, but Joe is injured, and probably not only a little bit. We don't know in the moment, we sent him home so we have to see, but it's his ankle yes."
Burnley's opening goal, scored by Jack Cork, had a suspicion of offside while the midfielder tucked home from close range after Ashley Barnes won the ball in a challenge with Alisson.
"I couldn't see that, of course not," Klopp said of the offside decision.
"Not 100 per cent sure but Alisson said to me he had the ball. I don't know what that means exactly, I need to watch it back, I don't know."
Liverpool made seven changes but the introduction of Firmino and Mohamed Salah from the bench with the score at 1-1 was key, victory moving the Reds back to within two points of Manchester City in the Premier League title race.
"Lots of players needed more time to warm up and it was fair, a proper fight," Klopp said.
"They scored their goal from a set piece which does not make life easier.
"Striking them back was exceptional in the circumstances. I really like that, this is massive tonight."