The Hoops finished in 21st place in the league phase to set up a daunting playoff tie with the German giants in their first Champions League knockout round appearance since 2012-13.
The underdogs thought they had got off the perfect start when Nicolas Kuhn drilled a low strike past Manuel Neuer inside 25 seconds, only for the effort to be chalked off for offside against Adam Idah.
The game soon fell into a pattern that was expected beforehand, with Bayern enjoying large swathes of possession to push Celtic back towards their own.
The pressure eventually told when Michael Olise fired his left-foot shot into the top corner to give Vincent Kompany's side a half-time lead, before Celtic were punished in the opening stages of the second period for giving Harry Kane the space to volley home from a corner.
With over 40 minutes left to play, the Hoops would have been fearing a sizeable defeat, but to their credit, they battled their way back into the contest to create the opening for Daizen Maeda to reduce the deficit in the 79th minute.
Try as they might, the Scottish champions could not find a leveller in the first leg of their knockout round playoff tie, although they will retain some hope ahead of Tuesday's return fixture at the Allianz Arena.
SPORTS MOLE'S VERDICT
Celtic would have entered the contest desperate to establish a first-leg advantage ahead of a difficult trip to Germany next week.
However, in the end, they would have been relieved to still have a fighting chance after going 2-0 down before the game had even hit the 50th minute.
They would have been ruing the costly mistake of leaving Kane unmarked for Bayern's second, but they would have also taken inspiration from the fight and determination they showed to claw their way back into the first leg.
Brendan Rodgers will know his team have a mountain to climb in the second leg, but if they can negotiate the first 20 minutes at the Allianz Arena, they may start to grow in belief that they could pull off a surprise turnaround.
CELTIC VS. BAYERN MUNICH HIGHLIGHTS
Disallowed Kuhn goal vs. Bayern (1st min, Celtic 0-0 Bayern Munich)
Celtic have the ball in the net! Kuhn lets fly from the edge of the box, drilling a low shot past Neuer in the opening minute to spark scenes of jubilation around Celtic Park. Unfortunately for the hosts, their celebrations were cut short by the assistant's flag, before VAR confirmed that an offside Adam Idah had blocked Neuer's view.
Olise goal vs. Celtic (45th min, Celtic 0-1 Bayern Munich)
Celtic's resistance is broken just before the break. Olise drives inside after collecting Dayot Upamecano's long ball forward, before lashing an unstoppable strike into the top corner at the near post to leave the hosts deflated at the half-time interval.
Kane goal vs. Celtic (49th min, Celtic 0-2 Bayern Munich)
Kane gets his obligatory goal. The England captain punishes Celtic after being left free at the back post, volleying a controlled effort past Kasper Schmeichel from Joshua Kimmich's deep corner.
Maeda goal vs. Bayern (79th min, Celtic 1-2 Bayern Munich)
Celtic have a foothold! Joshua Kimmich heads a near-post corner looping into the air. Auston Trusty rises high to nod it back towards goal, before Yang Hyun-jun flicks it into Maeda's path for the forward to tuck home his fourth European goal of the season - the most any Celtic player has scored in a single Champions League campaign.
MAN OF THE MATCH - MICHAEL OLISE
Although he was withdrawn just after the hour mark, Olise probably did enough to earn the Man of the Match award, especially with his performance in the first period.
The former Crystal Palace winger offered a real threat from Bayern's right flank, creating a couple of chances and attempting three shots, including a thunderbolt to put the visitors in front.
Not only did he make a meaningful contribution to the match, but he added another highlight to a successful European campaign, having netted five goals in nine Champions League appearances this season.
CELTIC VS. BAYERN MUNICH MATCH STATS
Possession: Celtic 43%-57% Bayern
Shots: Celtic 9-10 Bayern
Shots on target: Celtic 2-5 Bayern
Corners: Celtic 7-7 Bayern
Fouls: Celtic 4-4 Bayern
BEST STATS
WHAT NEXT?
The Bavarians will take a narrow lead back to Germany, leaving Celtic with an almighty task in next Tuesday's second leg in Munich.
In the meantime, the Hoops will play host to Dundee United in Saturday's Scottish Premiership clash, while the Bundesliga leaders will look to negotiate a top-of-the-table clash against Bayer Leverkusen.
Written by
Ben Sully