Bayern won 4-3 on the night - and the quarterfinal 6-4 on aggregate. The flashpoint was Camavinga being sent off for two yellow cards, with his second for stopping Bayern from taking a quick free-kick.
Kane, who scored on the night, said afterwards: "After the break, we talked about how we needed to move the ball more, play with more composure, from side to side.
"Sometimes it's easy to go fast, but there wasn't enough space. Real Madrid didn't surprise me because they're always very dangerous in the Champions League. We knew their history in this competition and the quality they possess. They're very dangerous, and we had to play at our best in both matches to win.
On Camavinga's time-wasting, Kane added: "I think it's a red card, without a doubt, and considering both matches, I think we are deserved winners.
"I also believe that a Madrid goal shouldn't have stood because there was a foul at the start of the play by Rüdiger on Laimer that wasn't called."