Tomorrow, when the draw for the play-off round for the group stage takes place, their name will be prominent only by its absence.
The 2-0 defeat to Legia Warsaw in the second leg of their third qualifying round tie left them not only out of the competition - but deservedly so.
There can be no excuses. No hard luck stories. No if onlys.
The truth - as the embarrassing 6-1 aggregate confirms - is that they went to the well once too often, and found they had a large hole in their bucket.
The warning signs were there in last summer's qualification struggle, and underlined in the subsequent group stage collapse.
Nothing was done to even patch over the problems. And last night, at Murrayfield, they paid the heavy price.
Watched by a crowd of more than 30,000 - which included old Bhoys Davie Moyes and Malky Mackay, both heavily quoted in the race won by Ronny Deila to succeed Neil Lennon - they could not give the new boss "one of the greatest nights of his life" as he had predicted they would.
Instead, Deila has been left with a memory which will be seared on his mind, no matter how hard he tries to erase it. And when the draw for the play-off round takes place tomorrow, for Celtic and their fans it will simply be a painful voyeuristic exercise in what might have been.
For Deila's Bhoys, the draw that now matters takes place an hour later when their name will be among the seeded teams in the hat for the Europa League play-off round.
That's when the realisation will hit home that jousting with giants in the Champions League is over before the schools have gone back.
Instead, the fare will be much less appetising, served up every Thursday, when they sit down with some teams they will have to look on the internet to identify.
That is assuming, of course, they can get past the play-off round for this competition.
The fans will need no reminding that in Lennon's first sojourn into Europe, four years ago, Braga had won by three clear goals in the first leg in Portugal.
The Hoops were fired up to make a dramatic comeback in the return.
But, like last night, the visitors sunk this notion by scoring the first goal.
And despite going down 2-1 on the night, sailed through to the play-offs while condemning Celtic to the Europa League's final knockout round for a place in the group stage.
There, Utrecht brought Europe to a complete halt for the season.
A repeat of those back-to-back knockouts would be more than most supporters could stomach and the consequences would continue throughout the European action-starved season.
THE repercussions are already set to be felt in the transfer market. Rather than extra quality being brought in, what already exists within the squad will be involved in a race for the exit door - led by Fraser Forster and Virgil van Dijk with Kris Commons and Adam Matthews possibly just behind
That's unlikely to be the end of "reconfiguration" of the assets as the black hole created by the absence of Champions League group stage games is addressed.
The pragmatic manager will quickly turn talk to building for next season's assault on qualification for the Champions League, a process which must begin with winning the SPFL Premiership title.
There is no danger Deila will not be permitted to stay long enough to see that job through.
The failure to steer safe passage back into the group stage was a situation undermined before he got anywhere near the coal face.
Sure, it's a huge black mark against his name, and a huge disappointment to him and everyone else connected with the club.
But the men who employed him know better than anyone that this accident was always one bad draw away and they can't revoke Deila's licence just because he was steering the company car when it happened.
What he needs now is backing, understanding and time.
Time to get his style embossed on the side and to get some key players, as yet still searching for full fitness and form, up to full speed.
That includes the likes of Mikael Lustig and Nir Biton, who missed most of the closing stages of last season after surgery and injury.
James Forrest is another playing catch-up - his appearance as a sub for Anthony Stokes for the closing 20 minutes last night was his first action since March 1.
Scott Brown is still two months away from making his comeback after rupturing a hamstring in pre-season, and the captain's absence continues to leave a major void in the team.
Deila did shuffle his pack for this game. But, while the personnel changed, the problems remained the same. And - as in Warsaw - when Legia scored, the goals were of the cheap variety and eminently avoidable.
The first and most damaging came after 36 minutes.
Losing possession inside Legia's half saw the central defence reacting by stepping up towards the halfway line.
A quick ball through the middle by the omnipotent maestro, Michal Kucharczyk, started a foot race between Emilio Izaguirre and Michal Zyro.
The Honduran was goal-side and thus favourite, but the youngster outmuscled him and got clear to shoot low past the advancing Forster. The tops came off the Legia fans. The bottom fell out of the Celtic world.
While this killer goal had not looked to be coming, neither had Celtic given the impression they were about to score and dig out a foothold in this tie.
Considering what was at stake, their lack of urgency was as surprising as it was disappointing, and Legia's goal saw support turn to spleen-venting on the part of some who came to see a fightback and found themselves witnessing a surrender.
Indeed, it took Celtic 17 minutes to get a shot off. And, by half-time, Charlie Mulgrew's effort was the only save Dusan Kuciak had been called upon to make.
Sure, the keeper had been troubled by a series of corners. But they were aimed into areas, not at targets, and brought nothing by way of an effort on goal.
When Legia scored a second on the hour mark - Kucharcyzk having a simple task from close range after Izaguirre had lost possession on the left side of the defence - for Celtic, the Edinburgh saying "You'll have had your tea" was replaced by "Your tea's oot".