After scoring 73 times for club and country in the 2025-26 season and his "magical" award win, Kane switched focus back to soccer but had a rare off-day on Saturday (Sunday AEDT), which left Bayern and Dortmund level on points at the top of the Bundesliga.
"It's something you have to deal with when you're at the top, deal with the emotions, deal with everything that comes with it," Kane said. "I felt like I handled it well. Of course not the best day today, but that's life, you move on."
Elsewhere in Europe, Christian Pulisic's goal set AC Milan on course for a 3-1 win over Inter Milan in the latest edition of their city rivalry, and Barcelona bounced back from two bruising losses by dismantling Alaves 6-1.
Bayern honoured Kane before kick-off as he showed off the trophy with his family on the field to cheers from the crowd.
Kane hit a penalty against the crossbar and hit the post on another chance, but did set up Bayern's second goal with a smart header that left Dayot Upamecano an easy finish.
Fabio Silva cancelled that out with an 89th-minute leveller for Dortmund.
Bayern were without coach Vincent Kompany, who was resting after he was released from hospital following a sudden collapse last week.
In Italy, Diego Moreira weighed in with two assists and a goal in an impressive first half for the Belgium international as Milan inflicted Inter's first defeat of the season.
Moreira whipped in a cross for Pulisic to head Milan into the lead in the fourth minute and delivered the corner from which Adrien Rabiot doubled the Rossoneri's advantage six minutes later.
Alessandro Bastoni pulled one back for Inter, but Moreira got on the scoresheet himself with a free kick shortly before halftime.
Milan moved up to fourth, four points behind joint leaders Inter and Lazio, who can move clear atop Serie A at home to Cagliari on Sunday (Monday AEDT).
Third-placed Roma beat struggling Udinese 5-2, and Bologna beat Monza 2-1.
In Spain, Lamine Yamal and Raphinha scored twice each as Barcelona cruised to a 6-1 win over Alaves and took back top spot in La Liga from Atletico Madrid.
Barcelona were coming off losses to Paris Saint-Germain and Real Madrid, but victory never seemed in doubt against an overmatched Alaves.
Raphinha moved to 15 goals from 10 La Liga games, four ahead of Real Madrid's Kylian Mbappe. Anthony Gordon and FermÃn Lopez also scored for Barcelona.
Atletico were on top for only a few hours after beating Levante 2-0 earlier.
In France, Troyes beat Le Mans 2-0 in the only Ligue 1 game of the day after three others were moved because of protests across the country.
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