To retain an interest in the tournament they almost certainly needed a bonus-point win, but the possibility of any sort of victory was dynamited by a performance in which their basic skills and decision-making abilities seemed to desert them.
To rub salty embarrassment in Glasgow's wounded pride, they were beaten by a Cardiff Blues side that was so far short of full strength that it was closer to their second team than their first. The Blues may have maddened the Scotstoun crowd with some of their time-wasting tactics, but at least in that policy they showed a degree of intelligence that was conspicuous only by its absence from the Warriors display.
It was understandable, in the circumstances, that Glasgow should want to play a high tempo game, but that urgency seemed to cloud their thinking as well, as a succession of moves fell apart, undone by execrable handling. When they did have an extended period of pressure towards the end of the first half, they made nothing of it, a failure that was all the more glaring as they had a man advantage for most of that time.
After their loss at Arms Park last weekend, the Glasgow players had stressed that this was no exercise in revenge or atonement, but there was certainly a commitment to, and aggression in, the early contacts that had been all too lacking in Cardiff.
That vigour earned the Warriors a couple of early penalties, albeit too far from the Blues' posts for them to threaten the scoreboard. Distance was no object to Rhys Patchell, however, for when the Blues were awarded a penalty near their own 10m line in the sixth minute, the centre - last week's man of the match - stepped up and whacked the ball fully 62 metres and straight through the posts. Astonishingly, it cleared the crossbar with a few feet to spare.
While the Scotstoun crowd rubbed their eyes, the Glasgow players seemed equally discomfited by the monster strike, as they made a stream of handling errors. The consequence was that Cardiff could pretty much dictate the game's geography in that opening quarter.
There was a suspicion that Glasgow's composure was no better than it had been in Cardiff. They were certainly looking after the ball a little better, but even if they were not coughing it up at the breakdown they still found ways to make life easy for their visitors. Six minutes after watching Halfpenny's first penalty effort sail wide, they gifted him another chance with a silly infringement at a lineout. This time, the Lions full-back made no mistake.
At least they did seem to have an edge in the scrum, and they tried to make that advantage tell just short of the half-hour mark when they were awarded a penalty near the Cardiff line and opted for the set-piece instead. At the third formation, the Warriors pack piled forward, the Blues crumpling at the onslaught. There was a strong case for a penalty try, and although referee Pascal Gauzere was not persuaded he sent Blues prop Sam Hobbs to the sin bin.
It should have been the breakthrough Glasgow needed, but they could not take advantage of that prolonged visit to the Cardiff 22. A few phases later, they did send Niko Matawalu over, but Gauzere, on the advice of the television match official, decreed that Rob Harley had illegally cleared a path for the scrum-half and chalked the score off. It was a hugely controversial call, and derision poured from the stands in the wake of it as Cardiff closed out the half with their 6-0 lead still intact.
It hardly helped that Glasgow captain Al Kellock had clearly been struggling with an arm injury throughout the first half. Josh Strauss took over from Kellock temporarily, and that change was made permanent when the teams came back out for the second half.
But the scrappiness of Glasgow's play continued to draw groans from their supporters. Their attempts to put pace and width on the ball were undermined by their own anxieties. The crispness and precision that illuminated their play last season was nowhere to be seen.
As the hour mark loomed, and that big fat zero was still stuck on Glasgow's side of the scoreboard, it was obvious that the five-point win they craved was not going to happen. Indeed, a win of any sort was looking increasingly unlikely, and the prospects looked bleaker still when Ruaridh Jackson sent a penalty effort wide of the posts.
By contrast, Halfpenny made no mistake with his effort, five minutes later, to put Cardiff 9-0 ahead. Glasgow's response was to empty their bench, and the introduction of Chris Cusiter finally gave them a presence on the scoreboard when, in a swarming 70th minute attack, the little scrum-half slipped a clever inside pass to Ryan Grant, who steamed over between the posts.
That, though, was where it ended for Glasgow. Duncan Weir had a chance to win it with a 78th minute penalty, but his attempt also went adrift. As, indeed, had Glasgow's European ambitions by then.