Harry Kane continued his successful start to life with Bayern Munich in Wednesday's Champions League win over Manchester united, but late defensive slip-ups showed Thomas Tuchel's side remains a work in progress.

Bayern led 2-0 at halftime and 3-1 with two minutes remaining, but only just held on to win 4-3 after a late United rally.

The late lapse was similar to Bayern's 2-2 home draw with Bayer Leverkusen on Friday, where the German champions twice led but were pegged back – eventually sharing the spoils after a late injury time penalty.

Kane, who famously has yet to win a trophy in his career, was open about his desire for team success as a motivation for his move to Bayern.

Bayern broke the bank to bring Kane to Germany, spending 100 million euros ($108 million) to smash their transfer record.

But like Bayern, who have won the past 11 Bundesliga titles, Kane's lust for silverware will not be satisfied with domestic success.

Since defeating Paris Saint-Germain in the Champions League final in 2020, Bayern have been eliminated at the quarterfinal stage in each of the past three seasons.

On the evidence of Wednesday night's late loss of concentration, the side still has significant room for improvement, particularly in a match-up with Pep Guardiola's Manchester City juggernaut.

'BIG PRICE TAG'

Before the match, Tuchel told reporters "with time (Kane) will make the players around him better. He will learn how to make them shine."

The England captain's impact was telling early and it was fitting that Leroy Sane, a player reborn this season with five goals in his last seven matches for club and country, would be the one to benefit.

After scoring a second-half penalty against United, Kane has five goals from five Bayern starts, while also proving a creative presence in build-up play.

The England captain spoke openly about his "price tag" after the match, acknowledging the expectations placed on him, both from inside and outside the German champions.

"Whenever there is a big price tag on your name, there is expectation and you want to repay the club who has put faith in you," Kane said.

"It's been really good to start the way I have. It's a big competition and we are one of the favourites but first of all we need to get the job done in the group."

The six-time European champions have now won 20 opening Champions League fixtures in a row.

In that time, they had conceded just two goals – one fewer than they conceded in the second-half on Wednesday.

Bayern will face sterner challenges than Erik ten Hag's struggling Manchester United.

"It was a good start here tonight," said Kane. "Come the new year, hopefully we are in a good place and can look forward to those knockout games."