The German said: "When players are sliding in like that it can get unsafe, because of the speed, and somebody has to say stop with these tackles".
The Reds overturned a second-half deficit to triumph 3-1 on the road, though victory came at a cost as defender Joe Gomez suffered a fractured left leg during the first half.
"Joe is injured and probably not only a little bit". You get the ball, nice, but it's like bowling.More news: Apple's official iPhone XR Clear Case is finally here
Dyche sent his best wishes to the 21-year-old but insisted Mee had done nothing wrong.
The Reds boss clashed with Burnley counterpart Sean Dyche after the injury, saying: "I said to the referee after the first sliding tackle over six or seven yards, when he got the ball and everyone liked it: 'Please, tell them they can not do that".More news: Merkel ally Annegret Kramp-Karrenbauer wins race for CDU leader
He said: "He [Klopp] didn't reference Daniel Sturridge's cheating when he went down, nothing near him, and he got a free-kick for it".
In response to Klopp's comments about the Clarets' rough approach, Dyche said: "Of course football managers can question whatever they like but I don't think they can reinvent the rules". I imagine a player who seems to be an honest player, in Gomez, realised that.
That is the view of Sky Sports pundit Paul Merson, who says that the Reds MUST win their game with Bournemouth (12.30) to put the pressure on City. Although, it was such a blow to lose Lewis Cook to that bad injury - and a real shame for him.More news: Deontay Wilder Confirms Fury Rematch: 'I Can't Wait for Wilder-Fury2'
Dyche said the Klopp didn't mention one particular issue when the managers seemingly exchanged some heated words following the match.