Liverpool forward Sturridge was accused of diving as the Reds swept past Burnley in their Premier League clash on Wednesday night.
Speaking after a high-octane game at Turf Moore, Dyche hit out at the England international by saying: “I was a little confused. I couldn’t make out what part of that was right and wrong.
“What I would say is this, and I think it’s important to register, there were some excellent tackles last night.
“I think the only one that was questionable was from Bardo [Phil Bardsley]. 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.
“He [Klopp] didn’t reference Daniel Sturridge’s cheating when he went down, nothing near him, and he got a free-kick for it.”
But Klopp has hit back at Dyche now.
The Liverpool boss said: “Daniel Sturridge is not a cheat.
“I’m not sure whether he (Dyche) spoke about the challenge of Bardsley on Moreno. What can I say?
“Sometimes a striker expects a tackle and tries to avoid it by jumping.”
Klopp also provided an injury update on Gomez.
“It’s just a shame for the boy,” the Liverpool manager added.
“He’s been in outstanding shape. He has helped us a lot.
“It could have been worse.
“Six weeks is massive for us, but it means he will be back for a big part of the season and that’s good.”