A 12th win means second-placed Liverpool have made their best-ever start to a top-flight season after 15 games but Klopp revealed his plea to match officials to protect his players from a series of robust sliding challenges from the Clarets was largely ignored.
Joe Gomez faces a spell on the sidelines after the England defender was carried off early in the 3-1 win at Turf Moor, which cut Manchester City’s advantage at the top to two points.
Gomez will have scans on an injured left ankle following a full-blooded challenge from defender Ben Mee.
“Burnley had a specific plan to be really aggressive and really physical,” said Liverpool’s German boss.
“Joe is injured, and probably not only a little bit. We have to see what he’s like. We don’t know at the moment and we have to see tomorrow. It’s his ankle.”
Burnley manager Sean Dyche made no apologies for his side’s approach as the hosts picked up just one yellow card, but Klopp added: “I’m pretty sure saying this won’t make me a lot of friends here, but that’s not the job I have.
“I said (to the officials) after the first challenge, I don’t know who did it, but it was like a sliding challenge where the player came in from six or seven yards and gets the ball. Everybody likes it but I said to them ‘please, tell them they can’t do that’.
“The referees have to make sure it doesn’t happen. You get the ball, nice, but then, boom, you get the player as well.
– Klopp warning –
“It’s like (10-pin) bowling and that’s exactly what happened four or five times. It was no foul but you have to be careful if you’re going in at full speed. I told the ref he needed to calm it down because the danger of injury is always there and we had to make a substitution of an really important player for us.
“You can be aggressive, that’s OK and it’s part of football. Just be careful. Sliding six or seven yards to win the ball, these times are over and somebody needs to tell you to stop doing it.”
Klopp’s decision to make seven changes from the Merseyside derby victory over Everton almost backfired until goals from James Milner, substitute Roberto Firmino with his first touch, and Xherdan Shaqiri sealed a comeback win after Jack Cork had given the hosts the lead early in the second-half.
Burnley are only kept off the bottom of the table on goal difference after taking two points from the past 24.
Following his 300th game in management, Dyche played-down suggestions of a spat with Klopp at the final whistle, insisting: “I just said to him ‘well done’. That was it. The reaction from our supporters at the end showed me they are still very much with us and that display was more like the standards we know we’re capable of.”