Erik ten Hag's side will feel the Group A encounter got away from us, as seven goals were scored in Bavaria, including three in a frantic finale.
Leroy Sane's shot evaded Andre Onana's grasp to make the breakthrough and, four minutes later, Serge Gnabry doubled the advantage to hand the Bundesliga giants a two-goal lead at the interval.
Although Rasmus Hojlund pulled one back with his first goal for the Reds, any hopes of a comeback were quickly extinguished when the VAR advised referee Glenn Nyberg to view his screen to see a handball by Christian Eriksen, when he could not get out of the way of a Dayot Upamecano header deep beyond the far post.