The German giants won 2-1 in Glasgow in the first leg of the play-off tie on Wednesday (12.02.25) and the striker was pleased with how the team withstood pressure from the Scottish champions towards the end of the game.
Speaking to TNT Sports, Kane said: "Whenever you win a game like this, you're always pleased because it's not an easy place to come.
"There were definitely areas in the game in which we could have done better and we'll need to improve for next week, but overall we scored at the right times.
"They put us under pressure at the end and we had to stay strong, which we did.
"We knew the atmosphere would help them at the start of the game and they nearly scored after a minute. We had to be patient, we knew we'd have more of the ball. Sometimes you need a bit of special quality to open a game like this up."
Meanwhile, Kane still retains the ambition to begin a career in the NFL one day but is focused on winning silverware with Bayern first.
The England captain said: "I've been asked about it before and my focus is on here, the Champions League, Bayern Munich, but it's something I'd like to explore in a future date.
"But I still feel like I've got many more years ahead of me."
Kane watched last weekend's Super Bowl between the Philadelphia Eagles and Kansas City Chiefs and was happy with the result as Chiefs quarterback Patrick Mahomes missed the chance to close in on his hero Tom Brady's record of seven championship wins.
He said: "All credit to the Eagles, stopping the Chiefs doing the three-peat. I'm backing my boy Brady, so it was nice to see it if I'm totally honest."