The German said: "When players are sliding in like that it can get risky, because of the speed, and somebody has to say stop with these tackles".
The injury represents a significant blow to Klopp, who had complained to the match officials about the manner of Burnley's sliding tackles before Gomez was caught by Ben Mee's follow through in the 20th minute.
"Joe is injured and probably not only a little bit".
"I just can't believe Jurgen Klopp and Liverpool fans - and I don't believe they do - would want cheating in the game and sacrifice good, honest challenges".
Gomez was clattered into the advertising hoardings at Turf Moor after Mee's tackle and Klopp criticised referee Stuart Attwell for being too lenient with Burnley's players. "I couldn't make out what part of that was right and wrong", Dyche told the media.More news: Diogo Dalot: Manchester United hosting Fulham a 'big game' after winless run
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".
"We send him our best if there is any injury 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".
"And I thought we were effective in the way we mixed it - not enough - you have to win a game - but we've got to get back to being us, and get back to the consistency of being us".
"Our lads went about their business terrifically last night and everyone else apart from the manager seemed to agree", he added.