Bayern Munich must follow their 2-1 victory over RB Leipzig with a winning run to get their season back on track, forward Harry Kane said.

Kane scored twice against Leipzig on Saturday, including a late winner that broke Bayern's three-game losing streak across all competitions, bringing hope back to the club after a turbulent week marked by the announcement of coach Thomas Tuchel's imminent departure at the end of season.

"We need to keep doing what we're doing. It was good to win this game but we need to go on a run until the end of the year," Kane told reporters.

"We had to show a reaction after last week. We have a responsibility to the club and our manager, we can't just sit there and sulk about it."

The 30-year-old added that he had practiced Saturday's opening goal with forward Jamal Musiala during training and he hopes to build better connections with his team mates after Tuchel said Kane was unhappy with the service at Bayern last week.

"We need more connections with each other, the last few weeks we have not had it but we can build on (what we achieved) today," Kane said.

Kane leads with 27 goals in the Bundesliga and 31 in all competitions this season. Bayern trail the unbeaten Bayer Leverkusen by eight points, who are currently at the top on 61 points after their 2-1 win over Mainz 05 on Friday.

"The season isn't going like we wanted it to go, credit to Leverkusen," Kane said of the gap between the teams on top. "We need to keep fighting and we need to push them."

Bayern host Lazio in the second leg of their Champions League last-16 tie on March 5 and visit Freiburg in the Bundesliga on Friday.