Dragons can still reach the Challenge Cup quarter-finals despite a hammering in Castres, who now top Pool 1.
The hosts scored six tries with Thomas Fortunel, Anthony Jelonch and Wilfrid Hounkpatin touching down before the break.
Julien Dumora converted all Castres' tries and began the move that led to Thomas Combezou's bonus point score.
Dumora added the next and Jared Rosser scored consolations either side of Kevin Firmin's final Castres' try.
However, Dean Ryan's Dragons can still reach the knock-out phase.
They have a home match on Friday against Russian minnows Enisei-STM (20:00 GMT) to round off their group campaign and can top the group if Castres slip up at Worcester at the same time.
Hill back
The Welsh side could also qualify for the quarter-finals as one of the best second-placed sides.
Wales lock Cory Hill returned from illness to captain Dragons while fly-half Jacob Botica earned a first start, albeit at a full-back amid injury problems.
Rio Dyer again replaced the injured Ashton Hewitt on the wing and Lloyd Fairbrother was at loose-head prop, with Brok Harris suspended.
All five previous encounters between the two sides had gone with home advantage, the Dragons losing 32-29 on their most recent visit to Castres in 2015.
Rosser's run
Castres have not lost at home in Europe for more than four years and Dragons never threatened that record as the hosts dominated from the opening whistle.
Their mix of power and pace was too much for a Dragons team, who have been much-improved this season.
There was a bright moment for the visitors via Rosser's solo score.
He gathered a loose ball in his own 22 and set off before kicking ahead and winning the foot-race before taking a kind bounce to touch down.
Dragons battled to the end and Rosser's outstretched arm rewarded their efforts at the death while Sam Davies converted both his scores.
Dragons director of rugby Dean Ryan told BBC Sport Wales:
"We had some moments we needed to nail down in the first 40 minutes against a fully-loaded Castres side at home.
"We knew if we kept the pace high we'd get chances, but the risk is (making) errors; the first 40 had everything apart from us getting over the line.
"The Dragons are a young, thin squad, we've had a hectic period and it's hurting us.
"Our strongest available side (against Enisei on Friday) is just about who's fit after a very physical game. We've got some bruised bodies."
Castres Olympique: Dumora; Nakosi, Combezou, David, Paris; Fortunel, Kockott; Tierney, Jenneker, Hounkpatin, Jacquet, Moreaux, Delaporte (capt), Jelonch, Tulou.
Replacements: Firmin, Benedittis, Wihongi, Samson, Gerondeau, Radosavljevic, Vialelle, Laveau,
Dragons: Botica; Rosser, Griffiths, Dixon, Dyer; S Davies, Knoyle; Fairbrother, Dee, Brown, J Davies, Screech, Hill (capt), Basham, Moriarty.
Replacements: Shipp, Reynolds, Coleman, M Williams, Keddie, R Williams, Robson, Penny.
Referee: JP Doyle (England).
Assistants: Mike Hudson (England) & Rob Warburton (England)
For the latest Welsh rugby union news follow @BBCScrumV on Twitter.