The England international netted four times in Thursday's 6-1 rout to take his tally for the season to 26 and move two clear of Romelu Lukaku in the goalscoring charts.
Kane spoke of his desire to boost his numbers at King Power Stadium and is equally determined to add to his tally on the final day of the season and clinch a second Golden Boot in a row.
"First and foremost, we wanted to come here and put in a good performance and win," he told Sky Sports.
"Of course I'd been thinking a lot about getting on the scoresheet and it's the first time I've scored four goals [in a game]. It's a good moment to do it.
"I was hoping to get one or two goals at least and then hopefully take it into the next game. But now I'm in the driving seat.
"There's still one game left to play so I'm not resting on my laurels. I've got to go out against Hull and get four more, hopefully.
"I felt good. Leicester made it tough for us, they came out in the second half and really put the pressure on. For us to get that third [goal] was vital and then the game opened up.
"I started to cheat a bit, get a bit lazy and wait on the last man. It was one-v-one and two-v-two at the back and I fancied my chances."
Son Heung-min scored Spurs' other two in the rout, with Ben Chilwell netting what proved to be scant consolation for last season's champions.
Son, who set up Kane's opener in the first half, believes the 23-year-old would boast a formidable goal tally had he not been sidelined with ankle injury problems this term.
"I think the pressure was down, we enjoyed the night. Every player really enjoyed the game," said Son.
"I'm really happy for 'H' (Harry Kane) and I scored two goals, as well.
"It's very important to support him. I don't know how long he had an injury but he's still scored 26 goals. He's an unbelievable player, he can score from anywhere."