In the end, they managed to level the try count but only thanks to a touchdown registered after the outcome was decided.
"Clearly we're disappointed not to have produced the win we all wanted for a great home crowd," Gregor Townsend, the Glasgow coach, said. "The players battled very well the whole game long but we didn't play consistently enough over the piece to win."
The harsh reality, though, is that a club who had a chance of reaching the quarter-finals right up until their final match last season have gone backwards in being effectively eliminated after only two games this time.
Defeat was a bitter blow on what could have been a great night for the club. Warriors officials had been rightly proud to sell out this first Heineken Cup tie at Scotstoun since it became their home ground – the official attendance registered at 6194 – but a large part of the reason why was demonstrated as the supporters of European professional rugby's last unbeaten side this season made their presence felt.
Chants of "Ulster, Ulster," were interspersed with the "Stand up for the Ulstermen" anthem and the noisy visitors were rewarded as their team earned the first kickable penalty, However, from just inside his own half, as the rain began to teem down with real intensity, Paddy Jackson pulled his attempt just wide.
Thereafter, the early stages were marked by understandably cagey play from both side in treacherous conditions. Fourteen minutes in, Ulster were awarded another penalty eight metres inside their own half and wide on the right. Ruan Pienaar opted to shoot at goal but while his attempt was on target, it fell just short.
Glasgow's first chance came three minutes later as, not for the first time, they put Ulster's scrummage under pressure and forced an infringement. The crowd told us what had happened almost as soon as Peter Horne struck the ball, but that was merely a further reminder of how well represented the visitors were, with the supporters behind the goal at the leisure complex end of the ground almost exclusively from Ulster.
The home support found their voices soon afterwards. A near identical sequence of events gave the centre the chance to make amends and from Horne found his range this time.
The lead lasted just two minutes though. A clever chip in behind the Glasgow defensive line was brilliantly gathered by Byron McGuigan on the retreat, but he was tackled just as he reached the 22 metre line and hung on to the ball in contact, allowing Jackson to level the scores.
Ulster's intelligent tactical kicking again took its toll when Stuart Hogg slipped as he tried to field a bouncing ball in his 22. He conceded a lineout from which Ulster set up camp in the hosts' 22 and drew a penalty when a Glasgow forward strayed offside at a ruck, allowing Jackson to nudge his side in front for the first time.
Glasgow's cause was not aided when, having again gambled by having only two backs on the bench, they were once again forced to employ Fijian scrum-half and occasional back-three man Nikola Matawalu as a winger after McGuigan had to be helped off with a shoulder injury.
As the conditions eased, they got a chance to get back on level terms after Hogg took a quick tap penalty close to halfway and gained an extra 10 metres when Ulster defenders tackled him too soon, but Horne pulled his attempt wide.
Horne's inability to hit the target was becoming a serious issue and he sent another slapped effort wide just after the interval. His unhappy evening ended soon afterwards when he had to be helped from the field after being injured in a midfield collision. Scott Wight replaced him, leaving Glasgow no further back cover with 35 minutes remaining.
A lengthy passage of Ulster pressure ensued but Glasgow defended with real fire allied to discipline to protect their line. Pienaar did eventually get another shot at goal, but, from close to 60 metres away, did not quite get the distance.
Consequently, Ulster's next penalty was fired into the right corner rather than at the posts and from the lineout they set up a driving maul which finally saw them breach the Glasgow line as Chris Henry managed to squirm out of a tackle and touch down, his score confirmed by the TV replay judge then made to count fully by Jackson's conversion.
On what had looked like a night when a two-score deficit would prove irretrievable Glasgow soon went further behind when Jackson hit the target with his third penalty.
As the clock wound down the Ulster stand-off struck a fourth time to seal the win and nudge his team sufficiently clear that even when Matawalu rose well to collect Wight's cross kick and score in the corner, the unconverted score was insufficient to snatch even a bonus point.