Timo Werner guided in the opener 15 minutes from timeCeltic's hopes of Champions League progress are over after their profligacy was punished in a frustrating home defeat by RB Leipzig.
Matt O'Riley and Greg Taylor struck the woodwork in quick succession and Daizen Meada and Kyogo Furhashi also passed up glaring chances for the opener.
Leipzig showed the ruthless edge Celtic lacked with late goals from Timo Werner and substitute Emil Forsberg.
It leaves the Scottish champions bottom with one point from four games.
But while a top-two finish is now beyond Celtic, their hopes of salvaging a Europa League place were boosted by Real Madrid's late equaliser away to Shakhtar Donetsk, who are now four points ahead in third and visit Glasgow in a fortnight.
Celtic's group-stage failings were encapsulated in a dizzying sequence midway through the first half. O'Riley rattled the base of a post with a 20-yard strike and Taylor pounced on the loose ball only to scuff it on to the bar with the goal at his mercy.
Seconds later, Kyogo grazed the woodwork with a gilt-edged header from Sead Haksabanovic's delivery.
Maeda had set the tone of frustration in the opening seconds, scooping an awkward header inches over, and wasteful finishing is ultimately what has condemned Celtic to an exit with two games to spare.
They were eventually undone by a slick Leipzig outfit that had found Joe Hart in imposing form. The Celtic goalkeeper, who gifted a goal in last week's defeat in Germany, stuck out a leg to brilliantly divert Christopher Nkunku's powerful drive past a post then spread himself to foil Willi Orban.
Celtic looked increasingly ragged as the second half swung from end to end and the only surprise was how only it took for a goal to arrive. Leipzig full-back Mohamed Simakan blazed over at one end, Maeda volleyed Aaron Mooy's cross wide at the other.
But Leipzig's growing menace was rewarded when Werner guided a header from Andre Silva's drilled cross into the bottom corner.
Still Celtic had chances, with substitute Giorgos Giakoumakis unable to convert from close range.
But Leipzig put the result beyond doubt when Werner rolled a pass to Forsberg, who took a touch then sent an unerring finish into the top corner.
Player of the match - Timo Werner
A goal and assist made it an enjoyable return to the UK for the former Chelsea strikerGalling night for Celtic - analysis
A night that promised much for Celtic ends with a familiar pang of regret over missed chances and an unwanted Champions League record.
The Glasgow club have now equalled Monaco's mark of having lost seven consecutive home games in the group stage, a barren run stretching back to 2016.
Deprived of captain Callum McGregor through injury, Ange Postecoglou doubled down on his attacking philosophy and O'Riley impressed in a deeper midfield role that he's accustomed to. Left-back Taylor, too, shone as the hosts gave as good as they got for much of this contest.
The stats, though, are galling. Celtic racked up 16 shots, just two of them on target, and their XG (expected goals) of 1.75 amplifies their struggles to put the ball in the net. It became inevitable that Leipzig would not be so generous at the other end.
It leaves Celtic needing to win at home against Shakhtar and take a least a point in Madrid against an already-qualified Real to secure the consolation of Europa League football.
Match stats
Celtic have lost each of their last seven home Champions League games, equalling the longest run of home defeats by a team in the competition, previously set by Monaco between May 2017 and December 2018 (7). RB Leipzig secured their first-ever win in Scotland, after previously losing on the road to Celtic and Rangers (they won their previous three home games v Scottish sides).Celtic mustered 16 shots, their most without scoring in a Champions League game since November 2013 against Milan (20 shots, 0 goals).Celtic have failed to score in consecutive home games in Europe for the first time since October/November 2016 also in the Champions League group stages. RB Leipzig's Werner has been directly involved in seven goals in his last four away Champions League games, scoring four (1 for Leipzig, 3 for Chelsea) and assisting three (1 for Leipzig, 2 for Chelsea). Werner both scored and assisted in the same Champions League game for the fourth time and is the fifth player to manage that feat for RB Leipzig in the competition (also Sabitzer, Poulsen, Angelino and Nkunku).What's next?
Celtic host Hibernian in the Scottish Premiership on Saturday (15:00 GMT), the first of three domestic outings before their next Champions League assignment at home to Shakhtar on 25 October (20:00).
Line-ups
Celtic
Formation 4-2-3-1
1Hart
88Juranovic20Carter-Vickers6Jenz3Taylor
33O'Riley41Hatate
11Abada9Haksabanovic38Maeda
8Furuhashi
1Hart88JuranovicBooked at 90mins20Carter-Vickers6Jenz3Taylor33O'Riley41HatateBooked at 34minsSubstituted forMooyat 66'minutes11AbadaSubstituted forForrestat 42'minutes9HaksabanovicSubstituted forTurnbullat 66'minutes38MaedaSubstituted forBernabeiat 80'minutes8FuruhashiSubstituted forGiakoumakisat 66'minutesSubstitutes
7Giakoumakis13Mooy14Turnbull16McCarthy25Bernabei28Abildgaard29Bain31Siegrist35Robertson49Forrest56Ralston57WelshRB Leipzig
Formation 4-2-3-1
21Blaswich
2Simakan4Orbán32Gvardiol22Raum
8Haidara24Schlager
17Szoboszlai18Nkunku11Werner
19André Silva
21Blaswich2SimakanSubstituted forHenrichsat 76'minutes4Orbán32Gvardiol22Raum8HaidaraSubstituted forDialloat 83'minutes24Schlager17SzoboszlaiSubstituted forForsbergat 76'minutes18NkunkuSubstituted forNovoaat 88'minutes11Werner19André SilvaSubstituted forPoulsenat 76'minutesSubstitutes
9Poulsen10Forsberg25Ba34Nickisch37Diallo38Novoa39Henrichs44KamplReferee:Halil Umut MelerAttendance:57,565Live Text
Match ends, Celtic 0, RB Leipzig 2.
Second Half ends, Celtic 0, RB Leipzig 2.
Josko Gvardiol (RB Leipzig) wins a free kick in the defensive half.
Foul by David Turnbull (Celtic).
Josip Juranovic (Celtic) is shown the yellow card.
Substitution, RB Leipzig. Hugo Novoa replaces Christopher Nkunku.
Corner, RB Leipzig. Conceded by Alexander Bernabei.
Attempt missed. David Turnbull (Celtic) right footed shot from outside the box is just a bit too high.
Attempt blocked. Aaron Mooy (Celtic) left footed shot from the centre of the box is blocked.
Attempt blocked. Giorgos Giakoumakis (Celtic) right footed shot from the centre of the box is blocked. Assisted by Matt O'Riley.
Goal! Celtic 0, RB Leipzig 2. Emil Forsberg (RB Leipzig) right footed shot from the centre of the box to the top right corner. Assisted by Timo Werner.
Substitution, RB Leipzig. Abdou Diallo replaces Amadou Haidara.
Attempt blocked. Josip Juranovic (Celtic) right footed shot from outside the box is blocked. Assisted by Alexander Bernabei.
Corner, Celtic. Conceded by Willi Orbán.
Attempt blocked. Giorgos Giakoumakis (Celtic) right footed shot from the centre of the box is blocked. Assisted by Aaron Mooy.
Substitution, Celtic. Alexander Bernabei replaces Daizen Maeda.
Attempt missed. Giorgos Giakoumakis (Celtic) header from the left side of the six yard box is close, but misses to the left. Assisted by James Forrest with a cross.
Attempt saved. Matt O'Riley (Celtic) left footed shot from the centre of the box is saved in the top centre of the goal. Assisted by Greg Taylor.
Hand ball by Giorgos Giakoumakis (Celtic).
Substitution, RB Leipzig. Yussuf Poulsen replaces André Silva.
