It was only the Scots' first match, but the history of this competition is not littered with teams who got off to losing starts and then recovered to qualify for the knockouts.
Some have done it, of course. Bath and Wasps didn't just lose their opening match in this competition last season - they lost their opening two. And yet they both made the quarter-finals.
In the story of how they did it, we see a glimpse of what Glasgow must do now in order to give themselves a chance of qualifying for that final eight.
Wasps beat Castres and Harlequins away from home to qualify as one of the best runners-up. Bath beat Montpellier and Toulouse away - with a four-try bonus point - to make it as group winners.
Those were major victories on the road and that is now the world that Glasgow have been plunged into in the wake of Saturday's loss to the Saints.
The reality of European rugby hit them right between the eyes.
The tea-leaves told us that Glasgow would win this. They had a stellar cast of international players. They had home advantage in the fortress of Scotstoun. And they had some form.
Northampton had few of those things. They had lost three of their four games in the Aviva Premiership, albeit by narrow margins. From last season's quarter-final team, they were missing the front-row of Alex Corbisiero, Dylan Hartley and Salesi Ma'afu, who is now on Toulon's books.
One of their go-to second-rows from last season, Samu Manoa, has also gone to Toulon and the other, Courtney Lawes, is injured.
This was a new Saints pack at Scotstoun and yet they were convincing winners in every department.
Glasgow had a beaten scrum and had a ropey line-out, they were second best in the collisions and error-prone at critical times.
Warriors can get away with some of these things - and occasionally many of these things - in the more merciful environment of the Pro12. Not so in Europe.
Certainly not against a team as rugged as Northampton, a side who spend their weekly lives engaged in dogfights in the Premiership. They were battle-hardened and clinical on Saturday in a way that Glasgow were not.
The scrum wasn't even a contest. Northampton won six penalties in that area.
They garnered six points and a sin-binning, which brought a converted try, from their overwhelming dominance in the scrum. Kieran Brookes, at tight-head, had a field day.
They looked like men with twin targets - not just Champions Cup but, for some, the Six Nations.
When Eddie Jones, the new England coach, gets a look at Brookes' performance, he's going to like what he sees. When he watches Luther Burrell, jettisoned by Stuart Lancaster, he's going to like it all the more. Burrell was top class.
Northampton drive on. They were tougher, physically and mentally, than Glasgow.
The group now looks like a scrap between them and Racing 92, who took five points from the Scarlets in Wales, unless Glasgow can find the kind of venom that typified the Saints.
It was sobering stuff for coach Gregor Townsend. It's been an age since a team came to his own backyard and beat them up like Northampton did.
In truth, there was a large element of self-harm about it as well.
The game was in its relative infancy when Glasgow's composure went out the window. In failing to get close to a garryowen, Stuart Hogg set a hare running, the hare going by the name of George Pisi, who ploughed over under the posts.
Then Glasgow's scrum came under fire. It went down, it went down, it went down.
Three scrum penalties inside 19 minutes and Ryan Grant in the bin for the third. This was a new kind of examination for Townsend's Pro12 champions.
The vulnerabilities carried on. Hogg missed a routine tackle on Ahsee Tuala and Saints were in again.
Peter Horne, that stand-up guy in the Glasgow midfield, scored a try of his own to cut the deficit to eight points, but Stephen Myler stretched it to 11 before the break.
Glasgow had enough ball to make a game of it. Even after Tuala scored his second try, the home team had a mountain of possession and any number of promising field positions.
Eventually they scored, through Josh Strauss, but there were so many butchered moments in there too. A maul shunted backwards out of the Northampton 22, a knock-on when momentum was building, a dreadful under-throw from their new Georgian hooker, Shalva Mamukashvili, at a line-out five metres from the Northampton line.
It was a recurring theme. Glasgow would inch forward, Scotstoun would rise to its feet and then Northampton would turn on the turbo defence and Glasgow would buckle.
The thunderous defence of the visitors didn't just repel Glasgow physically, it damaged them mentally. Their intensity got into the Glasgow psyche. Saints messed with their heads all day.
It was a deeply uncomfortable experience for the Pro12, in general, and, particularly, for those who believed in Glasgow's capacity to make the step up in Europe at last.
They have a mountain of work ahead of them if they are to be relevant in this tournament this season. The hope has not been extinguished, but it's flickering.
The Champions Cup is such unforgiving terrain that already Glasgow Warriors are looking ahead and trying to figure out what they might have to do to make amends for their wounding defeat to Northampton Saints at Scotstoun on Saturday.