Kane sent Gareth Southgate's side ahead in the Group C contest, with the Bayern Munich forward finishing into the back of the net from close range following a deflected cross from Kyle Walker.
However, Denmark proved to be the better team from that point forward, and the Danes levelled the scores with a long-range Morten Hjulmand strike in the 34th minute.
Kane's overall performance was criticised, with the 30-year-old often coming deep in a bid to receive the ball, meaning that England did not offer much of a threat behind the Denmark defence.
Ex-England forwards Gary Lineker and Alan Shearer were among those to criticise the team's performance at Euro 2024 last time out, and Kane has now hit back at the pundits who questioned the display.
England struggled to a draw with Denmark
"What ex-players or ex-players who are pundits now have got to realise is it is very hard not to listen to it now, especially for some players who are not used to it or some players who are new to the environment," Kane said during a press conference.
"I always feel like they [pundits] have a responsibility - I know they have got to be honest and give their opinion but also, they have a responsibility of being an ex-England player that a lot of players look up to. People do listen to them and people do care what they say.
"The bottom line is we haven't won anything as a nation for a long, long time and a lot of these players were part of that as well and they know how tough it is.
"So it is not digging anyone out. It is just the reality that they do know it is tough to play in these major tournaments, and tough to play for England. I would never disrespect any ex-player.
"All I would say is, remember what it is like to wear the shirt and that their words are listened to. Some of the lads... I don't know how many, but we do hear it.
England remain on course to qualify for round of 16
"We all want to win a major tournament and I am sure they want us to win a major tournament, and being as helpful as they can and building the lads up with confidence would be a much better way of going about it."
England opened their Euro 2024 with a 1-0 victory over Serbia, before the 1-1 draw against Denmark moved them onto four points, which is enough to top Group C.
The Three Lions need to avoid defeat in their final group fixture against Slovenia on Tuesday to ensure that they will be present in the knockout round of the competition.
However, if Denmark fail to beat Serbia, Southgate's side would qualify even if they lose, while four points would also almost certainly be enough to see them advance as one of the best third-placed sides.
There are likely to be changes to the starting XI for the clash against Slovenia, with Trent Alexander-Arnold widely expected to lose his starting role in the middle of midfield.