Instead, the stat they must live with is that they crashed en route to the group stage not once, but twice, in the same month.
The reprieve handed to them after they had been dumped out of the third qualifying round by Legia Warsaw was allowed to slip through their fingers - along with a cheque for £15million.
The 1-1 draw they earned in the first leg of their play-off in Slovenia could not be capitalised upon as they went down 1-0 at home to a scrappy second half-goal from Tavares.
Now, instead of seeing their name in tomorrow's draw for the Champions League, they will have to wait until Friday when they will be included in the group stage of the Europa League.
It is scant consolation - if that - and will have ramifications for the rest of the season, not least in terms of players coming, and those going.
Champions League involvement is the fulcrum around which Celtic's business plan revolves.
Without the money it generates, the Green Machine struggles, and has to be cranked back a few gears.
Ronny Deila insists this is a long-term project. But, for Celtic managers, time is no friend.
His side huffed and puffed last night, but could not blow open the door to the promised land.
They had survived play-offs in each of the past two season. Their luck ran out on this occasion, Perhaps they used it all up in the Legia affair.
No one needed reminding of the near-heart attack-inducing drama which was last season's play-off second leg, when the Hoops came back from 2-0 down in Kazakhstan to win 3-0 in front of a frenzied home crowd to go through to the group stage.
However, of the XI who started that night under Neil Lennon, sales, departures, injuries and form meant that, incredibly, only Charlie Mulgrew, Efe Ambrose, Mikael Lustig and Anthony Stokes were handed the responsibility to once again see the side safely over the line and into tomorrow's draw.
The scorer of the all-important opening goal against Shakhter, Kris Commons, had to start on the bench, as he was when the teams drew 1-1 in Slovenia, before appearing at half-time for the ineffective Beram Kayal.
To go without last season's top scorer was a decision which showed Deila is his own man, focused on the future, not the past.
By the same token, his action in electing to call upon the Commons touch for the second half showed he was reactive when Plan A wasn't working.
The move to drop Jason Denayer and reinstate Ambrose to right-back with Lustig shifting into central defence alongside Virgil van Dijk, was another big call, given how well the teenage loan star has played since arriving from Manchester City, and how flaky the Nigerian's track record is on the big occasions.
It was the only change Deila made from the first leg starting line-up, betraying the fact that, though they had the comfort of home, the manager was still acutely aware Maribor had the potential to steal in and get away with the family silver - or Champions League gold.
How right he was.
However, despite the formation, Maribor still got through, with Agim Ibraimi shooting just wide and Tavares left incredulous when Craig Gordon saved from Mitja Viler, and the ball broke off the striker straight back into the grateful keeper's arms.
Gordon was also the hero when Dare Vrsic got through midway through the second half, the man recalled to the Scotland squad showing why by saving with his legs.
It was all adding to the tension which could only be relieved by a goal - preferably two.
Euro goal hero, Callum McGregor, thought he had provided it when, following a 1-2 between Anthony Stokes and Jo Inge Berget, he met the striker's cross and smacked a shot off the crossbar.
Celtic certainly looked a more cohesive unit with Commons involved. But the realisation of what was at stake intensified each time the visitors got near the Celtic goal, and hearts were not so much pounding as in mouths.
As in Maribor, the failure to close down the powerful and creative Zeljko Filipovic in the centre of the park was a major problem.
By contrast to the elegant Slovene, Celtic were too often wasteful in possession, to the chagrin of Deila and the consternation of the crowd.
Ironically, Celtic had looked better than at any time in the match when Maribor dealt them the fateful blow with 15 minutes remaining.
With Lustig replaced by Derk Boerrigter after suffering a groin injury, Emilio Izaguirre was left with the responsibility of trying to head clear a dipping cross from the left.
The ball did not clear the box, and eventually fell to Tavares who looped his shot over Gordon.
Ambrose had the chance to equalise and take the game to extra time when he met a Stokes free kick six yards out, but headed wide.
By then, Gordon had made another good save, this time from Jean-Phillipe Mendy as Celtic tried to push forward.
Van Dijk could have saved the day in injury time, but could not get the ball past a now-inspired Jasmin Handanovic.
Now, as they reflect on a golden opportunity squandered, the entire team must wonder what the rest of this season holds, where it will take them, and which players will be gone before that particular journey goes any further.