Thomas Muller was left "disappointed, angry and upset" after Bayern Munich's unbeaten start to Julian Nagelsmann's tenure was brought to an end with a shock 2-1 loss to Eintracht Frankfurt.

Bayern had gone 10 without defeat in competitive games since Nagelsmann replaced Hansi Flick, winning the last nine of those, but they came unstuck at Allianz Arena on Sunday.

Leon Goretzka deservedly put the reigning champions in front, only for Martin Hinteregger to equalise before half-time and Filip Kostic to secure a smash-and-grab win late on.

Kevin Trapp produced 10 saves to keep Frankfurt in the match, with Bayern only finding the net from one of their 20 shots, compared to two goals from five efforts for the visitors.

Muller created a game-high five big chances, but he was left to reflect on a rare home league loss – Bayern's first in 31 matches in a run spanning back to November 2019.

"We are disappointed, angry and upset," Muller told DAZN. "We definitely shouldn't have lost this game. We lacked effectiveness.

"We felt we had a lot of scoring chances, but the crucial centimetre was missing. Frankfurt scored from their first shot and their two goals in the end were enough."

Bayern suffered a rare home loss against Frankfurt

Bayern are now level on points with Bayer Leverkusen at the summit heading into the two-week break after falling just short of making it a perfect 10 wins from 10 since their opening-game draw, and Nagelsmann rued his side's profligacy in front of goal.

"Defeats always hurt and today's defeat was very avoidable," he told DAZN. "We had enough chances to score.

"In the end we conceded a classic Kostic goal, which was absolutely avoidable. Kevin Trapp played a very good game. We had good chances and didn't take them so we lost.

"When you look at the stats we had 20 shots against five to them. It doesn't matter if we deserved more because in the end we lost.

"Now we have to analyse what wrong and look forward to the next game in Leverkusen after the international break."

21 - Eintracht Frankfurt have won their first Bundesliga away game at FC Bayern Munich for 21 years - back in November 2000, they had celebrated a 2-1-win with Felix Magath in charge. Liberation. #FCBSGE pic.twitter.com/vrggCaUJww
— OptaFranz (@OptaFranz) October 3, 2021

Frankfurt's victory was their first of the Bundesliga season and their first away to Bayern in the league since 2000 when Felix Magath was in charge.

The shock triumph would not have been possible if not for Trapp, whose 10 saves was the joint-most in a single game this campaign in Europe's top five leagues.

Only Oliver Baumann for Hoffenheim against Borussia Dortmund and Sascha Burchert for Greuther Furth versus Stuttgart can match that impressive save count.

"I had a lot of work to do today," Trapp told DAZN. "We defended very well. Nobody seriously believed we would get something from Bayern today.

"We were a bit lucky, of course. We got the maximum out of what was possible. Our plan worked out very well in the end."