Kane hopes Lazio win the 'turning point' in Bayern's season
"It's been a good season so far in terms of the goals but as a team we know we can do better."
Bayern came into Tuesday's match having won just one in five games, a run which included losing the first leg 1-0 in Rome and also caused them to fall 10 points behind league leaders Bayer Leverkusen in the Bundesliga.
The run cost manager Thomas Tuchel his job, with the club and coach issuing a statement saying he would end his contract early in the summer.
Kane, who has scored at a remarkable rate despite Bayern's struggles, notched a brace in the win and now has 33 goals in 32 games in all competitions since arriving in the summer.
Speaking to reporters after the victory while holding the man of the match trophy and a schnitzel burger, Kane said he hoped it was "a turning point for the rest of the year".
"If we perform like that in most games we're going to come out with a victory. It was a pleasing day," said the England international.
"It's been a good season so far in terms of the goals but as a team we know we can do better."
"I'm trying to help that situation, the team are trying to help that situation, and I hope we can use this as a turning point to push on in the Bundesliga and see if we can put pressure on Leverkusen –- and see who we can get in the next round of the Champions League."
Coach Tuchel told Amazon Prime he had injured himself during his pre-match motivational speech.
"I don't know if the players know about it, they might have wondered why I sat for 90 minutes, but that's why."
"We've got very big goals and the minimum goal for all of us is the quarter-final," Tuchel, who won the Champions League with Chelsea in 2021, told reporters.
Bayern veteran Thomas Mueller said qualifying for the last eight was "not salvation... but a very important step" for the under-fire club.
The 34-year-old, who has at times called out his side's struggles, told Amazon Prime the win showed the season was not over for the German champions.
"I've said it before -- it's not a complete shambles here, we're sticking together off the pitch, we've just had a few footballing problems on it.
"We know how important it was to progress today."