The Bavarians, who have dropped to third in the Bundesliga after last week's 0-0 draw at bottom-placed Freiburg, conceded an 86th-minute goal after missing a string of clear chances against the Swiss.
"We need to wake up. We have reached a critical moment in the season for us now," Bayern CEO Karl-Heinz Rummenigge told his players at the club's traditional post-game dinner in the early hours of Thursday.
"You must now play aggressively and pull the old adage of 'all for one and one for all' out of the magic hat, and it all starts this Sunday, gentlemen.
"We must turn this corner quickly," he said. "We must all work together to pull ourselves out of this mess that we played ourselves into."
Bayern's world was still in order until the winter break, having advanced in the Champions League and the German Cup while also leading the Bundesliga.
In an erratic start to the year, however, they have won only two of their five league games as champions Borussia Dortmund gradually pulled away at the top.
"We had wonderful times earlier this season. We had a good Christmas but we are worried and concerned with what has happened since then," Rummenigge said.
The defeat in Switzerland means the Germans need to beat Basel, who also defeated Manchester United in this season's competition, by at least two goals on March 13 in Munich to advance in 90 minutes.
Any other result would mean them missing out on the biggest European club prize in a year when the final is held in Munich in May.
"I think a 1-0 result is one that still gives us chances to progress," said Bayern chairman Uli Hoeness. "I am not at all concerned that we might not make it in the return leg but we need to bring peace and quiet back into the club."
It would not be the first time Bayern had pulled themselves from the brink of elimination.
After being written off, the four-time winners won their last two Champions League group games in the 2009/10 season and eventually reached the competition's final.
Any slip-up against in-form Schalke 04 in the league on Sunday, however, will further increase pressure on Jupp Heynckes's team with their aura of invincibility from earlier this season long punctured.
"We had imagined it differently," said Bayern keeper Manuel Neuer, who pulled off several spectacular saves to deny the Swiss before Valentin Stocker's late strike.
"We are stuck in a difficult situation and in this phase we had imagined our game to be different. We must turn things around now," Neuer added.
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