In Neil Lennon's three full seasons as manager they have been knocked out of Europe in August, and then in December, and this season in March. In Utrecht, Udinese and then Juventus it has taken progressively better sides to finish them off.
By extending their survival Lennon has – over the course of his 24 European matches – redrawn the way the club is perceived on the continent. Heavy defeats are painful and it was a sombre Celtic party which flew back from Turin to Glasgow yesterday after losing 5-0 on aggregate to Juventus. Over two legs their defending was badly exposed as Juventus outclassed them. Celtic need not allow that to detract from a deeply rewarding overall European campaign, though, one which lifted them back to the status they enjoyed when Martin O'Neill and then Gordon Strachan were in charge. The Champions League is a rodeo and Celtic stayed on as long as anyone could have realistically expected.
Champions League money and excitement sustain Celtic now, in the stands, the boardroom, the dressing room and the manager's office. Finding a path through the qualifying rounds remains a tense annual ordeal yet the Uefa president Michel Platini has done the Scottish champions a great favour by reshaping the qualifying rounds. It means Celtic must play the champions of average countries rather than the fourth best team from the likes of Spain, England, Germany or Italy. That amounts to the difference between a Helsingborgs and an Arsenal.
Celtic must play in the second qualifying round, the third qualifying round and then the play-off round in order to reach next season's group stage (forgive the assumption that they win the SPL). They need not be daunted by that. A lack of match fitness will make them vulnerable when they first play on July 16 or 17 but they were seeded last year and will be again. That should spare them the most dangerous clubs in the qualifiers, such as the champions of Israel, Croatia, Romania, Serbia and the Czech Republic. Under the format introduced by Platini it is reasonable for Celtic to tentatively expect they will be back in the group stage later this year.
"Getting through every year is such a difficult thing to do," said Lennon. "You're two or three weeks into your pre-season and then you've got the qualifiers. I think it's a huge ask. Maybe further down the line, if the co-efficient gets better, it might make it easier but we are the fourth team to do it in the last 10 years. That's not bad for a league the size of ours. In the Helsingborgs games this season, both legs, the pressure was incredible. There was a spell in the first leg when we were under severe pressure. We overcame that and it was a huge relief to qualify."
The campaign came to be defined by the two epic matches against Barcelona but, before that, Celtic's confidence was forged by a goalless home draw with Benfica and a 3-2 win at Spartak Moscow. Suddenly the team who had never won an away group game was off and running. "We were finding our feet against Benfica and then obviously the huge lift was winning in Moscow. "
No Scottish team has made in beyond the last 16 in the modern incarnation of the Champions League and Celtic falling so heavily to Juventus confirmed that the glass ceiling remains. Is that as far as the SPL champions will ever go? "It depends on the draw I think," said Lennon. "If you get the luck of the draw, there are some other teams I think we're on a par with like Galatasaray and Schalke. But the gulf in size of squads, and the money they've spent, is big."
It is more realistic for Celtic to anticipate a return to the group stage next season than to think that they will get through this summer without being cherry-picked of their best players. The Champions League has allowed Victor Wanyama, Gary Hooper, Fraser Forster and Lennon himself to deliver a prolonged advertisement of their abilities. Wanyama and Hooper seem certain to leave. European nights provide spikes of excitement in Celtic's season, perhaps up to a dozen of them, but that must compete with the lure of the Barclays Premier League and its constant, 38-game razzmatazz. Lennon has certainly contemplated a time when challenging himself against Manchester United, Manchester City, Chelsea, Arsenal and the rest will eclipse the annual tightrope walk of trying to get Celtic into, and then out of, the Champions League group stage.
Reaching the last 16, beating Barcelona and winning an away game in the group has empowered this impressive, maturing Celtic manager. He has devoured the experience of challenging himself in the Champions League. It all started, remember, by going 1-0 down at home to Helsinki back in July. "Firstly I have proved I can manage at this level. Second, we have proved we can compete very well at this level. The football we have played at times has been of a very high order. We just came up a short in some areas against Juventus and there's no shame in that.
"There is satisfaction as a coach because there were so many question marks hanging over my head. Even when I took the job, 'rookie manager' was thrown at me for a long time. Once you win the league, that gives you a bit of comfort in a job like this. Then obviously the qualification into the group stages was massive. I felt we had a good enough team to compete and we have certainly done that. We just ran out of legs a bit. We just don't have a big enough squad to contend against the likes of Juventus.
"There have been some heroic performances in Europe this season, like the goalkeeper's. I thought Kelvin Wilson was unbelievable in Turin. He was just outstanding, England class. If there are any continental clubs looking at him, or even Premier League clubs looking at him, I thought he was just unbelievable against top, top quality opposition. It would be difficult to say that this group would be together again if we do qualify next year. [If we lose some] you've got to go and try to find quality players. We've got money, we've got the experience of this season and we've got a club that's robust and going the right way. So it's an exciting proposition for a lot of players.
"A lot of players are happy here. Joe Ledley is happy. Brownie [Scott Brown] is happy. Adam Matthews is enjoying his football here. Kelvin has had a fantastic season. But it's difficult to stop the progress sometimes, the ambitions, and I understand that."
"If anyone is leaving this summer I would hope to at least keep them for next season's qualifying rounds. If we could do that it would help because the players know our methods. That's something we can look at. It's hard to keep such a high strike rate when it comes to recruiting good players because everyone looks at what we do and will copy or try to overtake it. But I've got a great recruitment office with John Park at the head of it. He's always working, 24/7. It's a constant turning-of-the-wheel."
Celtic's next European date is June 24 when the draw is made to reveal their first opponents. Next season's final is in Lisbon, the first to be held there since 1967. They must set their sights lower these days, but the past few months have shown that Celtic's Champions League addiction is as powerful as ever.