But that has drawn a stinging response from Dyche, who claimed that England striker Sturridge dived to win a free-kick in the first 15 minutes of Wednesday's game.
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.
“Now if that's gone and been replaced by cheating, I'm absolutely happy to be old fashioned.
“There's no way I'd want to not see good proper professionals challenging in the manner that ours did last night, and replace it with cheating."
Liverpool lost Joe Gomez to an ankle injury after a first-half challenge from Ben Mee, but Dyche said the only tackle that Klopp had any right to complain about was one from Phil Bardsley on Alberto Moreno.
Dyche said: “What I would say is this, and I think it's important to register: there were some excellent tackles in the game.
“I think the only one that was questionable was Bardo's. I think Ben Mee's was a fantastic tackle.
“I imagine a player who seems to be an honest player, in Gomez, realised that. That was the message we got after.
“We send him our best if any injury has occurred but it wasn't from a bad tackle."