Kane won this season's Golden Boot with 25 goals, one more than Leicester's Jamie Vardy and Manchester City's Sergio Aguero, but the forward said personal glory was overshadowed by his side's woeful finish.
"It would have been nicer to have won the golden boot on a better day," Kane, who was named in England's preliminary squad for Euro 2016 on Monday, told British media.
"For me, it's a little bit of a good feeling but overall I'm gutted we haven't finished the season off strong.
"That definitely makes it harder because we know how much it means to the fans and how much it means to the club. When people think Arsenal had a bad season and we've had a good one, yet they still finish above us, it hurts."
Finishing third puts the club into next season's Champions League but Kane said that while Spurs were making progress they had a long road ahead of them.
"Games like Newcastle and the last few weeks show there's still a lot of work to do. We haven't cracked it yet," he added.
"We're still learning, we still have to work hard and we still have to improve. But everything is in place so we all have to try to stay positive – us, the fans, the club – because we're moving in the right direction."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Peter Rutherford)
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