Mauricio Pochettino's men sealed a spot in the last 16 after a 3-1 victory over holders Madrid at Wembley on Thursday (AEDT).
A brace from Dele Alli and a Christian Eriksen strike led Spurs to their win, which kept them top of Group H.
Kane, who made his return from a hamstring injury as part of the starting line-up, is confident Tottenham have proved they can overcome anyone.
"There is a long way to go. We've still got two more group games, we'll see how we cope with that and then see who we get in the next round," Kane said.
"We feel like we can beat anyone.
"In the Champions League, you have to beat the best teams to go far and that's what we'll try and do."
Spurs are back in action with a Premier League clash against Crystal Palace on Sunday.