Injured Kane was in the stands as his side produced another stunning comeback to reach the Champions League final.
Spurs trailed 1-0 from the first leg in north London before goals from Matthijs de Ligt and Hakim Ziyech appeared to take the tie beyond the north London side.
But a hat-trick from Lucas Moura sent Spurs through to the final against Liverpool.
Kane also said he hopes to be back for the final in Madrid.
Asked if he will be fit to face Liverpool, Kane told BT Sport, “Hopefully. Rehab is going well. I start straight-line running this week, that explains that run.
“Lucas scored a hat-trick though. We beat City and beat Ajax so I will have to train even harder and prove myself to try and get in the team!”
Kane went into the dressing room at half-time and has provided an insight into Mauricio Pochettino’s instructions to his side.
“I went down there at half-time. We knew it wasn’t good enough,” he added.
“We said there’s 45 minutes to give everything, we only have one more game left and don’t have to worry about being tired.
“Over the two legs, we probably didn’t play as well as hoped. Liverpool found a way against Barcelona and so did we.”
