Bayern officially ceded the title to Xabi Alonso's Bayer Leverkusen on Sunday, breaking their 11-year streak as champions.
Bayern are now staring at a first trophyless season since 2012.
The England captain, still without a trophy in his career despite an array of stellar personal records, said Champions League glory would give the season a different face.
"It's no secret here that the club sets out to win the Champions League every season," he told reporters.
"You know, from the club's point of view, it will be a failed season if we don't win anything this year because we're expected to win," Kane said, describing it as the "harsh reality of winning and losing."
"We still have the opportunity to turn the season into a great season if we win the Champions League.
"The motivation is still there for us as players. If we can do something special tomorrow night of course that keeps that hope alive."
Bayern and Kane returned from north London after a 2-2 draw at the Emirates. The abolition of the away goal rule means one team needs to win on Wednesday to reach the final four.
Kane moved to Bayern in the summer from Tottenham, Arsenal's north London rivals. He played his entire career at Spurs, having been released from the Gunners academy as a child.
At Tottenham, he scored 14 goals in 19 games against Arsenal, and added another in Bayern's visit last week.
"Maybe it is in the back of my mind that I was released at a young age (by Arsenal) there was a point to prove and I'm the kind of player who has had points to prove throughout my career," he said.
"I don't think that ever leaves you. That will always be in my DNA until I'm retired.
"Now I'm here at Bayern Munich and of course I have history with them (Arsenal) but all I can try and do is help Bayern Munich qualify for the semi-finals of the Champions League."
Bayern coach Thomas Tuchel confirmed Manuel Neuer and Leroy Sane, who missed the weekend's league win over Cologne, would return. Serge Gnabry and Kingsley Coman will be missing through injury, while Alphonso Davies is suspended.
"We have one decisive match to make the next step in this beautiful competition and we're determined to bring everything to the table," Tuchel said.
