That defeat came four days after last week's 1-0 loss to league title rivals Borussia Dortmund.
Bayern, who have now managed just two wins in their last six league matches, were knocked off top spot and into second place -- for the first time in 14 months -- by RB Leipzig, three points clear on 27.
"We have to turn the corner and we have to do it now," captain Philipp Lahm warned. "We are making just too many mistakes and paying the price. It is not a crisis but we have to cut back on those mistakes as quickly as possible.
"We seem to be a bit too carefree in our game. I do not know why that is. We have to analyse it. We are just not focused enough."
Coach Carlo Ancelotti's team are far from the dominant Bayern under his predecessor Pep Guardiola, with the backline less solid.
Central defender Jerome Boateng, Germany's 2016 player of the year, had his share of the blame in two of Rostov's goals, his once imperious presence repeatedly a step too late for the opponents.
"Jerome has to find his balance again," Bayern CEO Karl-Heinz Rummenigge said. "There is a bit too much hype around him at the moment. It would be good for him and the club if he came back down to earth a bit."
"It makes no sense to make a big fuss now," Rummenigge added. "The team knows that it has not played well. We must now do it better, starting on Saturday against Leverkusen."
Their opponents, who also qualified for the Champions League knockout stage, are as unpredictable as ever.
Capable of beating most teams on a good day, Roger Schmidt's players have also squandered points along the way, conceding late goals, like the 3-2 winner for Leipzig last week to drop to ninth in the Bundesliga.
Third-placed Borussia Dortmund, buoyed by the win over Bayern and their record-breaking 8-4 demolition of Legia Warsaw in the Champions League, travel to Eintracht Frankfurt.
Surprise leaders Leipzig can temporarily open up a six-point gap with victory at Freiburg on Friday.
(Editing by Sudipto Ganguly)
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