Spurs host Borussia Dortmund tonight as both teams begin the race to escape Group H, which also features reigning champions Real Madrid and Cypriots APOEL.
Kane has hit more than 20 goals in the Premier League for three seasons in a row and his last two totals of 25 and 29 have been enough to earn him the Golden Boot.
But the England striker now has Europe's premier competition in his sights, starting against Dortmund at Wembley.
"I have said before I want to break into that world-class bracket. To do that you have to play well in the Champions League," Kane said.
"The Champions League is a big stage, all the best players in Europe, if not the world, are here.
"And to be the best you have to produce your best against the best. I have six group games to prove that by hopefully scoring as many goals as possible and performing well."
After failing to progress from a relatively kind group last year that included CSKA Moscow, Leverkusen and Monaco, Spurs boss Mauricio Pochettino reflected his squad had struggled to cope with the additional physical and mental demands of the Champions League.
They are one season wiser this year and with the likes of Davinson Sanchez, Fernando Llorente and Serge Aurier added over the summer, their squad may be deeper too.
"Last season was our first experience of the Champions League - previously we play Europa League, for 98, 99 per cent of the players, and for myself too," Pochettino said.
"That experience [of last season] is important. We know very well what the competition demands from you, and I think that is so important.
"It was a very painful experience because we could not be at the level we should have been but today, it's not an excuse. We know that (the Dortmund clash) will be very tough. We need to be ready to compete at a higher level."