In the quest for a Champions League group stage place, that means putting their supporters - and manager, Ronny Deila - through the full gamut of emotions.
The 1-1 draw in their play-off first leg tie against NK Maribor was the perfect illustration.
Given a platform by an early goal from Callum McGregor then quickly conceding an equaliser, scored by Damjan Bohar, they made enough chances to make the second leg in Glasgow on Tuesday a comfortable cruise to the group stage draw two days later.
However, they also afforded enough opportunities to Maribor to have lost this game, and had the acrobatic form of 31-year-old Craig Gordon to thank for emerging with the tie level.
You just knew it was an important night when major shareholder, Dermot Desmond, joined the VIPs.
The Champions League theme tune booming out as the teams lined up - something Uefa do not permit until this round - was further proof Celtic are tantalisingly close to the Holy Grail of the group stage.
Of course, they have been here before.
It was a year to the day since Celtic were rocked by the 2-0 defeat they suffered at the hands of Shakhter Karagandy in the first leg of a play-off tie in Kazakhstan.
Neil Lennon's side did manage to pull that game around in the most dramatic fashion, with a 3-0 victory at Celtic Park.
It was, however, crucial they did not leave themselves with a similar mountain to climb this time.
After all, if you are only apportioned a certain amount of luck each season, it's fair to assume Celtic have already used up theirs - by dint of the way they got to this stage via a fateful administration transgression by Legia Warsaw.
The Europa League group stage awaits to provide a soft landing should Celtic fail to capitalise on this good fortune and crash out of Champions League qualification a second time this season.
However, while that would still guarantee European football through to mid-December, it would not guarantee the £15million cheque which winning through to Uefa's premier tournament brings.
That's a balance-sheet- shaping deposit Celtic have been grateful to bank for the past two seasons.
They had written it off after losing to Legia, until Uefa checked their rule book and provided the get-out-of-jail card Celtic have used to make it through to face NK Maribor in the play-off round.
What Uefa did not give Celtic was a ticket to the tournament proper. That is something they have to earn themselves.
But after the first leg of their play-off ended all square, and with a vital away goal, the chances of them making their ninth group stage appearance look bright.
Deila considered Maribor on a par with Legia. A warning, if any was needed, that the promised land may be in sight but access could still be denied.
The Slovenian champions must be respected and Deila did just that - acknowledging the formation he has favoured up to this point required tweaking towards caution and shoring up a midfield that had been badly exposed in the ties against Legia.
Kris Commons' attacking intention was sacrificed, Beram Kayal preferred for his defensive attributes.
The administrative kerfuffle surrounding Efe Ambrose's eligibility after suspension, and his late arrival in Slovenia as a consequence, was dismissed by Deila, though he decided to start with the Nigerian on the bench.
The chances are that the manager was always going to start with Jason Denayer alongside Virgil van Dijk, and with Swede Mikael Lustig at right-back.
The Ljudski vrt Stadium was an early test of the temperament of the Belgian teenager Denayer.
A section of one of the stands was empty except for a Uefa banner proclaiming "No To Racism" - part of the Maribor's punishment for unacceptable chanting by a section of their volatile fans at a previous qualifying tie against Bosnia's Zrinjski.
The kid showed no fear, standing up bravely to the challenge of helping Van Dijk contain the wily and mobile Tavares and Agim Ibraimi.
There was a breakdown in communication between the centre-backs, however, to allow Bohar to latch onto a through ball from Zeljko Filipovic and beat Gordon with a low shot.
That 14th-minute strike brought the scores level, after McGregor had scored his third away goal in Europe this season after just six minutes.
Stefan Johansen's intelligent pass had sent Jo Inge Berget in for a close-range shot, which was blocked, but the teenager's predatory instincts had led him to follow up and McGregor calmly shot home from close range.
It continued a wonderful run of important goals for the young midfielder, who scored in Reykjavik and Warsaw.
As in Poland, however, the Hoops could not hold on to this lead long enough to take control of the game.
They did have two efforts cleared off the line from corner kicks. Charlie Mulgrew saw his header nodded clear by Filipovic before Van Dijk looked on in disbelief as his header smacked team-mate Johansen in the face and went wide after the defender had risen high to beat the keeper.
Anthony Stokes believed he had a legitimate claim for a penalty early in the second half when his header was blocked by Aleksander Rajcevic, and the striker was even more vexed when a low shot crept just past a post.
Beram Kayal was brought down in the area under the nose of the fifth official but, again, his appeals were rebuffed.
It was clear both teams wanted to head to Celtic Park next week with a lead.
Johansen will wonder how he did not provide it for Celtic. He burst clear of the defence but mis-controlled the ball and Handanovic took it off his foot.
Despite the belts-and-braces midfield approach from the Hoops, which saw Ambrose finally enter the fray in place of Berget - but only after some confusion with the number board - Gordon was forced to make decent saves.
He denied Petar Stojanovic, Ibraimi and, most spectacularly, Ales Mertelj to maintain parity while Kayal might consider himself fortunate the referee did not award a spot- kick when Mitja Viler tumbled under his challenge.
Filipovic was at the heart of most of what Maribor did well, and Deila will undoubtedly demand he is given less freedom at Celtic Park.