The Three Lions had to settle for a 1-1 draw against Denmark, despite Kane giving them a first half lead.
Morten Hjulmand's magnificent strike gave Denmark parity, while they were the better side in the second half.
"It’s not just when we score that (we drop deep)," Kane, who was replaced by Ollie Watkins in the 70th minute, told reporters.
"It’s something we need to get better at. In general, when the teams drop a few players deeper we’re not sure how to the get the pressure on and who’s supposed to be going.
"In the second half we tried to change it a bit with me and Jude (Bellingham) playing in front of their two midfielders and then trying to get up. But it was difficult: credit to Denmark, they’re a really good side and they caused us some threats.
"We’re struggling with and without the ball. The pressing in both games hasn’t been quite right, and with the ball we haven’t been good enough – that’s from top to bottom, from me to Picks. Everyone's dropping below their level in terms of retaining the ball and playing under pressure. It was tough out there with the heat and the pitch. It wasn’t our greatest game but we got away with a draw."