With England trailing France 2-1 in Qatar, Kane, who had already scored a penalty in the match, squandered the chance to level by blazing his spot-kick over the crossbar.
"I'd say that was probably the worst that I felt in any moment," he told British media. "Obviously I've lost finals before. To have that responsibility, you almost feel like it fell on my shoulders.
"Not being able to execute something that I've been able to execute many a time in my career, I think that was the hardest part to process and take.
"In terms of that being my last memory (of a World Cup), yeah, I'm looking forward to the next World Cup to try and put that right, to try and go further. To try and lift the trophy as we all dream of doing."
England thrashed Latvia 5-0 on Tuesday to book their spot at the 2026 World Cup, with Kane scoring twice to take his international tally to 76 goals.
Asked if he could reach the century mark, the 32-year-old said: "The way I'm feeling right now, I'm not slowing down any time soon.
"The goals are there and the numbers speak for themselves. The way I feel on the pitch, the way I am seeing the game, physically and without the ball, pressing, I feel in a really good place."