Joe Gomez was injured in the game which Liverpool won 3-1 but Sean Dyche defended his team, saying he thought "some of the challenges were superb".
Klopp complained to fourth official Mike Dean during the game saying "the injury threat was massive" saying the potential threat was heightened by a wet surface at Turf Moor. It took the shine off Liverpool's 12th win in 15 league games.
"Joe's injured and probably not only a little bit," complained Klopp after the 21-year-old was carried off. "We won the game but the challenges from the beginning, the sliding tackling on that wet ground, I really think the referee should have said something earlier. The injury threat is massive. That was hard.
"Burnley had a specific plan, to be really aggressive in their challenges and stuff like that, so each ball they won, even if it was a throw-in for us, helped them and obviously didn’t help us mood-wise. So I was really happy we could just adjust a few tactical things [at half-time], but I told the players I shouted a lot in the first half but I wasn’t angry. I knew it could be a bit rusty, that’s how it is with a lot of changes, but now we are warm, used to it and we adjust a little bit.
"You get the ball, nice, but it's like bowling because you get the player as well. It happened four or five times. The first three or four challenges everybody likes it. I know that. It's part of football but it lead to the situation. Ok, no foul but Joe Gomez is injured."
Dyche reacted: "I thought some of the timing of the challenges were superb. That's part of that front-foot mentality, You've got to win the ball, you've got to challenge against these boys.
"You've got to put a marker on the game - not only with good tackles, but also with good play."