A 2-0 loss to Premier League rivals Liverpool in June's showpiece denied Spurs what would have been a first major trophy since 2008.
Goals from Mohamed Salah and Divock Origi gave Liverpool victory in Madrid, where Kane returned from injury but struggled to make an impact.
But Kane is hopeful the European run will not be a one-off for his side, who have moved to strengthen by bringing in Tanguy Ndombele from Lyon for a club-record fee.
"I think it just motivates you to get better," Kane told Sky Sports. "With the Champions League final, you want to play in those games all the time.
"We know it's going to be tough to get back there this year and it's down to us to perform."
Spurs finished the 2018-19 campaign fourth in the Premier League to guarantee themselves a place in the Champions League group stage.