Schmeichel beat away Harry Kane's deflected effort, Joshua Kimmich shot wide following Olise's cutback and the England captain missed Bayern's best first-half chance when he hit the bar from 16 yards after another pass from the right.
Bayern appeared to have more urgency in their pressing and were making most of the running but Celtic capitalised on some slack defending after substitute Adam Idah came deep to collect a forward pass and send the ball forward.
Celtic suffered the cruellest of Champions League exits after Alphonso Davies scrambled an equaliser for Bayern Munich in the final minute of stoppage time in the Allianz Arena.
Bayern Munich 1-1 Celtic (3-2 agg): Alphonso Davies’ stoppage time goal sent the German side through on aggregate.
Celtic kept the pressure on and Reo Hatate's first-time pass played Arne Engels in behind, but Maeda just could not reach the Belgian's low cross with the goal gaping.
