England meet Slovakia in the round of 16 on Sunday.
Kane said: "It is about just having that discipline in your positions, being in the areas where we are patient enough and can hurt them, and then really about being ruthless.
"I feel we’ve been ruthless on the defensive side, in terms of blocks and blocking crosses and winning balls and now it’s down to me, the attacking players and maybe the midfielders to maybe be a bit more ruthless in the final third of the pitch."
Kane added: "It’s the process of the tournament, naturally you get physically stronger, naturally you get sharper. We’ve had three games in a short space of time.
"I feel players get into their peak sharpness for knockout games and that’s what I have found in recent tournaments.
"Being the striker of the team, I want to score goals and help the team get through to the next round. Knockout football is a different prospect to the group stage, we have handled that well in the past and it’s time to do that again."