It is a bitter night for the club's supporters, who have had it pretty good in Europe in recent times. But what else is this defeat?
A disaster? A crucial pointer to life about to unfold under Ronny Deila? A sign of a switched-off, mismanaging club board?
Emphatically, it is none of these things. Not in the here and now. There is plenty hot air around Celtic these days but this Legia Warsaw setback tells us almost nothing of any significance.
Far more acute for Celtic are these days and weeks ahead. Fraser Forster, surely, will leave the club. So might Virgil van Dijk and Adam Matthews. The immediate issue is what kind of new team Deila can create.
Celtic losing out on a potential Champions League place is certainly a financial blow - we can come back to that. But, in terms of Deila's substance as the club's manager, these early days tell us little.
This is the question: will Deila be a good or bad Celtic manager? That is among the two or three essential issues that Celtic supporters and the media wish to know. Right now, early August 2014, is no time to be groping for an answer.
Was Neil Lennon a good Celtic manager? Most would say, yes, he was, especially given his European record at the club. Yet Lennon, in his early days in charge, might well have been written off.
I was with Celtic in Braga back in July, 2010, when Lennon's misery was compounded in that dire Champions League qualifying round second-leg.
A few weeks later, when Celtic capitulated 0-4 against Utrecht in Holland to miss out on the Europa League, things hardly looked rosy for Lennon in these early weeks in charge.
Yet any reliable judgement made about him then - just as with Deila now - would have been absurd. Months and years of telling evidence lay ahead.
Here's another question: is Celtic a football club being run poorly, or being mismanaged? Okay, let's look at a five-year cycle of evidence for an answer.
Celtic have played in the Champions League group-stage in each of the last two seasons. In five of the past six seasons the club has enjoyed European competition until Christmas or beyond. Three of these seasons were in the Champions League, two in the Europa League.
This is pretty decent. This looks to me like a football club that has got it right. A club that has taken its supporters on quite a few jaunts around the Continent.
Losing out on a potential £17m-plus Champions League bounty is certainly painful for Celtic. The club has thrived in recent seasons on such feasts. In fact, it's worth looking again at the Celtic finances.
If we are to believe the bare stats, Celtic are flush with money. In their last full-year accounts they boasted pre-tax profits of £10m, on turnover of £76m, and a net cash in bank for the year of a tidy £3.7m.
On top of lucrative Champions League monies raked in over the past two seasons, a further £17m was collected in the sales of Gary Hooper, Victor Wanyama and Kelvin Wilson.
Whatever way you view this, the running of Celtic has looked exemplary. The more so when you consider the catastrophe to have engulfed Rangers, and financial decisions at Ibrox which led to the dissolution of the old club.
It's hard to have it both ways with Celtic - yet many want to. The club is lauded - rightly - for its financial success story. Yet almost in the same breath CEO Peter Lawwell is harangued for being miserly and tight-fisted.
It seems odd that the Celtic board is both lauded and rebuked in the same sentence. Whatever the case about the team needing fresh and bold investment - and that means hard outlay - the last five years of strong stewardship cannot be disputed.
Over the next few days Celtic supporters will be highlighting an overly-cautious investment policy. Certainly, last summer, in such players as Amido Balde and Derk Boerrigter, it didn't look right. The club spread its little jam too thin.
But the greater evidence, of rude financial health and regular European football, has been a godsend to Celtic fans. The journey has been pretty enjoyable.
Like everyone else, I'm keen to know if Deila is going to be a Tony Mowbray or a Gordon Strachan (or even a Paul Le Guen). Right now, like everyone else, I haven't got a clue.
What I do know is that, to the toll of Artmedia, Braga and others, the name of Legia Warsaw can now be added. A sore one, triggering a minor crisis.