Beleaguered Celtic's Champions League hopes ended in the second qualifying round for the second consecutive year as a callow side were undone in extra time by Denmark's Midtjylland.
Raphael Onyedika side-footed home the crucial blow three minutes into the added period after Callum McGregor's stunning volley had put Celtic in front for the second time in the tie.
But defensive frailties cost them again as Awer Mabil levelled before Onyedika pounced to leave Celtic floored and bound for the Europa League.
They will face Czech side FK Jablonec in the third qualifying round next week, while Midtjylland go on to face PSV Eindhoven in European football's premier competition.
The result emphasises the scale of the task facing Ange Postecoglou as he attempts to rebuild a lightweight squad.
Celtic's pre-season has been dominated by talk from fans, pundits, and Postecoglou himself, about the lack of signings, with quarantine also denying them the services of recruits Carl Starfelt and Kyogo Furuhashi.
The fact they lined up with a defence with an average age of 21 told its own story, and the manager said it best this week when he referred to the team "flying by the seat of its pants".
But as in Glasgow last week they looked the more assured side in the first half, and McGregor provided the spark his team were searching for just two minutes into the second period as he took the ball on his chest before hooking it into the top right-hand corner.
The goal oozed class and gave Celtic the platform to kick on, and substitute James Forrest came so close to bolstering their advantage on the hour mark as he slid the ball wide after a good run.
And, just as in the first leg when Edouard passed up a one-on-one, they were punished for their profligacy. Midtjylland had not registered a shot by this point, but within two minutes of Forrest's effort, Mabil levelled.
The Australia international ghosted between Dane Murray and Greg Taylor to nod home a floated cross, emphasising the inexperience of the Celtic backline and the general anxiety which has surrounded the team in the last 12 months.
That only swelled from that moment on as the Danish side - roared on by about 6,000 of their fans - grew in confidence, and Victor Lind missed a golden chance to win the tie in stoppage time as he evaded 18-year-old Murray.
But Celtic were made to pay soon after as Evander floated in another delivery, which Henrik Dalsgaard steered into Onyedika's path, and the Nigerian had time to take a touch and dispatch from six yards out.
Man of the match - Evander
The Midtjylland number 10 was a danger with his quality deliveryWhat did we learn?
Celtic are as far away from being a Champions League group-stage club as they have been in a long time. Despite their decade of dominance in Scotland, they have drifted further from Europe's elite with every passing season.
It is fair to analyse the performance on the pitch, but only in the inescapable context of the squad Postecoglou has to work with.
To begin a Champions League qualifying campaign with a centre-back pairing aged 18 and 21, no clear first-choice full-backs or goalkeeper, and a striker in Edouard who clearly sees his future elsewhere is scarcely believable in the eyes of most Celtic fans. And that isn't even the full extent of their problems.
The club has no head of recruitment, no sporting director and are attempting their largest rebuild in two decades. Postecoglou says he walked into this job with his eyes wide open, and he will largely receive a pass in the circumstances, but with each passing game the scale of the challenge grows.
Across both legs there were signs of his high pressing, vertical style, but the Australian needs both time and signings to have any hope of success in the short to medium term. It's sure to be a bumpy ride.
What they said
Celtic manager Ange Postecoglou: "We just got tired in the end. They scored and got through it. I thought my players gave their maximum. It's the beginning of what we're trying to embark on. We controlled the game until they scored."
What's next?
Celtic don't have much time to shake off this latest blow as they open their Scottish Premiership campaign away to newly-promoted Hearts at Tynecastle on Saturday (20:00 BST).
Line-ups
FC Midtjylland
Formation 3-4-3
1Lössl
14Dalsgaard28Sviatchenko73Ferreira Júnior
6Andersson35Rigon Matos10da Silva Ferreira29da Silva
11Mabil74dos Santos Júnior7Sisto
1Lössl14Dalsgaard28Sviatchenko73Ferreira JúniorSubstituted forNicolaisenat 113'minutes6AnderssonSubstituted forCoolsat 105'minutes35Rigon MatosSubstituted forOnyedikaat 59'minutes10da Silva FerreiraBooked at 53mins29da SilvaSubstituted forDyhrat 89'minutes11MabilSubstituted forLindat 89'minutes74dos Santos JúniorBooked at 69minsSubstituted forHansenat 77'minutes7SistoBooked at 115minsSubstitutes
2Cools5Høegh16Ólafsson20Nicolaisen30Thompson37Onyedika43Madsen44Dyhr48Hansen53Lind54Fraulo58SimsirCeltic
Formation 4-3-3
29Bain
56Ralston57Welsh47Murray3Taylor
14Turnbull12Soro42McGregor
11Abada22Edouard17Christie
29Bain56Ralston57WelshBooked at 21mins47Murray3TaylorSubstituted forMontgomeryat 105'minutes14TurnbullSubstituted forAjetiat 105'minutesBooked at 108mins12SoroBooked at 76minsSubstituted forRogicat 98'minutes42McGregor11AbadaSubstituted forForrestat 59'minutes22EdouardBooked at 93mins17ChristieSubstitutes
1Barkas10Ajeti18Rogic23Bolingoli-Mbombo26Urhoghide30Shaw41Robertson45Doohan49Forrest54MontgomeryReferee:Bartosz FrankowskiLive Text
Match ends, FC Midtjylland 2, Celtic 1.
Second Half Extra Time ends, FC Midtjylland 2, Celtic 1.
Corner, FC Midtjylland. Conceded by Adam Montgomery.
Corner, FC Midtjylland. Conceded by Callum McGregor.
Corner, FC Midtjylland. Conceded by Scott Bain.
Attempt saved. Victor Lind (FC Midtjylland) right footed shot from the left side of the box is saved in the centre of the goal. Assisted by Evander.
Foul by Ryan Christie (Celtic).
Pione Sisto (FC Midtjylland) wins a free kick on the right wing.
Attempt missed. Erik Sviatchenko (FC Midtjylland) left footed shot from the centre of the box is close, but misses to the left following a corner.
Corner, FC Midtjylland. Conceded by Adam Montgomery.
Pione Sisto (FC Midtjylland) is shown the yellow card for a bad foul.
Albian Ajeti (Celtic) wins a free kick in the defensive half.
Foul by Pione Sisto (FC Midtjylland).
Substitution, FC Midtjylland. Rasmus Nicolaisen replaces Juninho.
Ryan Christie (Celtic) wins a free kick on the left wing.
Foul by Dion Cools (FC Midtjylland).
Albian Ajeti (Celtic) is shown the yellow card for a bad foul.
Foul by Albian Ajeti (Celtic).
Nikolas Dyhr (FC Midtjylland) wins a free kick in the defensive half.
Ryan Christie (Celtic) wins a free kick in the defensive half.