The match was a poor advert for European rugby - one of brutal frontal assaults relieved by long kicks and penalty awards and was little reward for the 3,348 spectators who turned up on a freezing night.
Ultimately it was decided by the boot with three successful penalties from Castres' Rory Kockott outdoing the pair from Glasgow's Scott Wight.
The tentative early stages saw Glasgow move into a 6-3 lead, early in the second quarter, thanks to a two out of two penalty kicking count from stand-off Wight.
Castres scrum-half Kockott, by contrast, had succeeded with only one from four, though an unsuccessful attempt did come back off the post.
But his fifth attempt, in the 36th minute, which was long and straight, was successful.
The sides went in after a first half that had failed to warm a chill Glasgow evening with the score tied at 6-6.
Both teams had had spells of possession but neither goal line had been seriously threatened thanks to determined tackling and referee Wayne Barnes detecting penalty offences.
Notably Glasgow had twice shot themselves in the foot at set scrums by engaging too early.
Glasgow made a livelier start to the second half but after 47 minutes Wight, in a moment which is sure to haunt him, was unable to take advantage of a penalty shot which was straight on from the Castres 22.
In turn Castres twice were unable to make anything of pressure situations on Glasgow's line and lost their advantage by conceding penalties.
With 57 minutes gone Kockott was able to nudge Castres into the lead with a long penalty.
The hard-fought exchanges appeared to have resulted in concern for Glasgow captain Al Kellock who went off late on with an arm injury.
With Glasgow unable to threaten further they saw their European hopes end as Castres held on to keep their alive.
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