"The group we had, a lot of people doubted us and we wanted to prove them wrong," Kane, who scored the equaliser in Tuesday's game, told reporters after the match.
"Hopefully we can build on this now for the rest of the campaign."
Tottenham manager Mauricio Pochettino praised his team and compared this season's tough draw to last year's, when Spurs dropped to the Europa League after failing to progress from a group consisting of AS Monaco, Bayer Leverkusen and CSKA Moscow.
Pochettino also said that the win in Dortmund was a good response to last weekend's 2-0 defeat by local rivals Arsenal in the Premier League.
"The reaction after Saturday was perfect," Pochettino told BT Sport. "The team stepped up and after Saturday, we were ready to compete here in a difficult game against a difficult team and we are so proud."
Tottenham, who are fourth in the Premier League, host bottom side APOEL Nicosia in their final Group H game in December with their immediate attention turning to Saturday's league fixture against 17th-placed West Bromwich Albion.
(Reporting by Aditi Prakash in Bengaluru)
