Castres had to rely on three penalties by scrum-half Rory Kockott to see off Glasgow 9-6 at Scotstoun Stadium on Friday.
The result sees Glasgow's Heineken Cup hopes extinguished as they failed to get the bonus point win they needed.
The French outfit headed into their latest Heineken Cup clash on the back of a 21-16 victory over Northampton, while Glasgow were looking to bounce back from back to back defeats to Leinster and Munster.
The Scottish outfit had failed to get over the tryline in each of their last two outings, and this match was to prove no different as the two teams contested a real war of attrition.
The Warriors enjoyed a bright start to the encounter and were able to apply early pressure to the Castres' line, though the attacks amounted to little as the visitors' defence held firm.
Castres were then able to mount an attack of their own, though Kockott pushed a resultant penalty wide, and the scores remained level until the 12th minute, when Scott Wight booted the hosts in front following a period of territorial dominance.
It took just nine minutes for the visitors to respond in kind through Kockott, though even less time for Glasgow to re-establish their lead courtesy of Wight's second three-pointer of the evening.
It remained at 6-3 until the dying minutes of the first half, when Kockott knocked over his second penalty after Glasgow had failed to relieve the pressure while in possession in their own half.
There was a similarly tight opening to the second period, with neither side appearing capable of taking a foothold in the match.
Though when Kockott kicked his third penalty of the night just before the hour, it established a lead that Castres would hold until the final whistle - despite desperate home attempts to force their way over the tryline in the final quarter.
Pens: Wight 2
Pens: Kockott 9
Glasgow: 15 Peter Murchie, 14 Tommy Seymour, 13 Stuart Hogg, 12 Peter Horne, 11 DTH van der Merwe, 10 Scott Wight, 9 Henry Pyrgos, 8 Josh Strauss, 7 John Barclay, 6 Rob Harley, 5 Al Kellock (c), 4 Tim Swinson, 3 Mike Cusack, 2 Dougie Hall, 1 Ryan Grant.
Replacements: 16 Pat Macarthur, 17 Moray Low, 18 Gordon Reid, 19 Tom Ryder, 20 Ryan Wilson, 21 Niko Matawalu, 22 Duncan Weir, 23 Sean Maitland.
Castres: 15 Romain Martial, 14 Marcel Garvey, 13 Seremaia Bai, 12 Rémi Lamerat, 11 Maxwell Evans, 10 Pierre Bernard, 9 Rory Kockott, 8 Antonie Claassen, 7 Jannie Bornman, 6 Ibrahim Diarra, 5 Christophe Samson, 4 Matthias Rolland, 3 Karena Wihongi, 2 Mathieu Bonello, 1 Yannick Forestier.
Replacements: 16 Marc-Antoine Rallier, 17 Mihaïta Lazar, 18 Anton Peikrishvili, 19 Pedrie Wannenburg, 20 Yannick Caballero, 21 Thomas Sanchou, 22 Paul Bonnefond, 23 Daniel Kirkpatrick.
Referee: Wayne Barnes (England)