Liverpool confirmed on Thursday that Gomez is set to be out for up to six weeks, meaning he will miss Liverpool's pivotal Champions League fixture with Napoli next week, as well as the home clash with Manchester United.
Dyche was responding to comments from Liverpool manager Jurgen Klopp regarding Burnley's tactics and the performance of referee Stuart Attwell.
However, speaking at his pre-match press conference, Klopp insisted that he can mitigate Gomez's loss and he has "a lot of players who can play that position".
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".
"It's just a shame for the boy", he said.
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The Englishman was accused of being a cheat by Burnley manager Sean Dyche.
"I think Ben Mee's was a fantastic tackle and I imagine that a player, who seems to me an honest player, like Gomes, I think he realised that. He would probably say it's possible but I think it's responsible that we have a little eye on that".
"He [Klopp] didn't reference Daniel Sturridge's cheating when he went down, nothing near him, and he got a free-kick for it".
"We all want to win football games, and there are different ways of doing it". We will see what we will do but we have other options of course.
But, before Klopp's comments, Dyche had spoken about his side's commitment in the tackle, and said: "I thought there were some excellent challenges".