Kane was one of a number of players who were criticised for their performances in the match that left England on four points after two games in Group C.
Former England strikers Lineker and Shearer analysed the performance on the BBC’s coverage before Lineker later used an expletive to describe the team’s performance on his Rest is Football podcast.
Speaking on the podcast on Monday, Lineker claimed journalists were “stirring the pot” while Shearer said England’s best response would be on the pitch.
“We’ve been critical of England’s performances, as has pretty much every journalist, but you know how it happens,” said Lineker.
“We’ve talked about this a few times before, about journalists not being brave enough to ask their own questions.
“I guarantee whoever that was was probably critical themselves. They do it a) to stir the pot and b) because they’re too scared to ask a question from their own selves.
“It puts Harry on the spot. I thought he answered it fine.
“There was one bit there where he says that we have responsibilities as ex-England players, that we should know better and that we never won anything or words to that effect.
“Fine, he’s absolutely right. But I will say one thing. The last thing in the world we want to be is downbeat and critical. We want the England team to perform well on the pitch. The best punditry of all is when England play well.”
Shearer added: “It’s important we never get personal. That’s the most important thing.
“They were terrible and we have to say that. If England were brilliant we’d say they were brilliant, that’s the way it is.
“As a player you always get the right of reply on the pitch. I have no problem what we said, I wouldn’t take anything back we said.
“England were really poor. I think the vast majority of the country, and even the boys in the squad, will know they were awful against Denmark. There were hardly any positives.”
England play Slovenia in their final game in Group C in Cologne on Tuesday (20:00 BST).