The Warriors saw their cup hopes extinguished as they failed to get the bonus point win they needed. Ultimately the contest was decided by the boot with three successful penalties from Castres' Rory Kockott outdoing the pair from Glasgow's Scott Wight.
Castres club director Patrick Alran said: "This is the first time that Castres have won an away match in the Heineken Cup. It keeps us in the running to qualify for the quarter-finals."
By contrast there was gloom in the home dressing room. Dejected coach Gregor Townsend accepted his side now had no chance of progressing and focused on the second-half effort, saying: "The second half was horrible. Between making errors and conceding penalties we couldn't get going.
"We did start to string together phases in the first half and at the pause they were shown in the dressing room where there were holes in the Castres defence. But they never got near to exploiting them because they couldn't get going."
The Castres win came down to the three penalties successfully kicked by scrum half Kockott to the pair by Wight but Alran highlighted the former's early misses.
"The team showed great spirit," he added. "n the first half they could have been put off by the three early misses out of four attempts by Rory. He is a player who usually has a 90 per cent record.
"Then in the second period they could not take two try scoring chances so right to the end Glasgow could have snatched a win. So they had to dig in throughout to keep their morale high."
Looking ahead to next week's return fixture, Alran concluded: "I am confident we can win but only if the players again are able to approach the game in a serious mood - there is a lot at stake."
This is not the case for Glasgow after a miserable night but Townsend promised a better performance. He said: "We can produce better rugby than that - we have done already this season. How we react to mistakes defines us as individuals and as a group. We owe it to the fans and to each other to put wrongs to rights next week."