Former Manchester United captain Roy Keane offered a scathing assessment of the Clarets' performance, with the 49-year-old saying on Sky Sports "I could play in that game" as they went in trailing 3-0 at half-time.
"He probably could have," Dyche said when asked about Keane's comments on Monday. "I don't know if you remember but he was pretty decent, to be fair. It wouldn't surprise me if he could have.
"I don't have a problem with people questioning us. It's part of their jobs. They're pundits for a reason, they have a voice, they have a say. Everyone has got an opinion.
"It's one of the strangest jobs where people are always telling you what you're doing wrong. I don't go to the doctors and tell him what he's doing wrong, or my lawyers, or my solicitors, but apparently with football managers everybody thinks they can do better than us.
"But I've no problem with Roy Keane or anybody else."
Keane was far from alone in questioning Burnley's performance as they were torn apart in the first half of the Premier League contest.
Dyche's side need to quickly put that game to one side, however, with Champions League-chasing Leicester visiting Turf Moor on Wednesday before Arsenal head north at the weekend.
"We don't park it without thought but it still needs to be parked," Dyche said.
"You've got to move on quickly. We talk about it, we analyse it and we make sense of it but the thinking on it has to go away quickly.
"They turned up and were clinical, and we weren't. We gave away too many soft goals. But we've been down those results before and I'm not worried about that side of it.
"I am worried about the injuries, we can't get everyone fit and we're coming up against a Leicester side who are having their fair share of it too.
"We've been having it for a long period now but we've come through that still putting wins on the board, still putting points on the board and we've stayed strong through this period."
There was some positive news on the injury front in the second half at Tottenham as Chris Wood and Dale Stephens both came on as substitutes as they return to fitness, but Erik Pieters, Robbie Brady, Ashley Barnes and Johann Berg Gudmundsson all remained out.
Brady and Berg Gudmundsson could return this week, although Dyche is trying to be cautious to avoid losing them for a longer period.
"With three (games) in a week it's a tough call," Dyche said. "They're close, especially Johann and Robbie, but it is tight. We just keep losing players constantly so we'll probably have to make a call on it and see if they're on the right side of it."