Harry Kane insisted Bayern Munich have further room for improvement after scoring four goals in their record-breaking 9-2 Champions League rout of Dinamo Zagreb.

Kane netted four times – including three from the penalty spot – as records tumbled in the Bavarian giants' first European outing under new boss Vincent Kompany.

Tuesday's four-goal haul took Kane to 33 Champions League goals, surpassing Wayne Rooney (30) as the top-scoring Englishman in the history of the competition.

It was the 24th hat-trick of Kane's professional career for club and country, while he became the first player to ever score three penalties in a single European Cup/Champions League game.

Bayern, meanwhile, are the first team to ever score nine times in a Champions League match, with Real Madrid being the last side to do so in the old European Cup in 1990 (9-1 versus Wacker Innsbruck).

Kane, however, told DAZN there are areas in which Bayern must improve, having been joined on the scoresheet by Michael Olise (twice), Leroy Sane and Leon Goretzka.

"It was an amazing game. The first half was really good, we took our chances," the England captain said.

"We didn't start the second half well and got caught from a couple of second balls. We'll have to learn from that. 

"Today we got away with that bad start in the second half, but against top opposition we could get punished for that.

"But the reaction afterwards was really good. It's great to score all these goals."

The only blot on Bayern's victory – which took them to the top of the Champions League's new 36-team league table – came as Manuel Neuer was substituted at half-time.

The goalkeeper had earlier appeared to be in discomfort after colliding with Zagreb striker Bruno Petkovic, but he played down concerns over his condition after the match.

Speaking to reporters in the mixed zone, Neuer said: "I collied there and I was a bit gone. 

"Then I hit a few balls and the pain stabbed me in the thigh. But it's nothing serious, a small matter."