Friday's defeat in a dismal display at Scotstoun left Glasgow rooted to the bottom of Pool 4 with any lingering hopes of qualification gone for another season.
The Warriors head coach told the Evening Times: "We must go to France and produce a performance that shows what wearing a Glasgow shirt is all about.
"The bottom line is Europe has now gone for another year but what is on the line is our pride.
"We know that Friday was unacceptable. We had the chance to provide a response to the defeat in Munster and we just did not take it, we let the Glasgow jersey and the support down badly.
"We know that we are out of the tournament and that is very disappointing, but at the same time we have to go out there and show what Glasgow Warriors are all about.
"Mistakes happen but the level we produced on Friday was simply not on. On top of that, Castres did not have to play well to win and that is very annoying.
"Yes it will be a challenging week and it will be about getting the balance right in how I try and get the best from them.
"But that is the role of the head coach in this situation, to make sure they do themselves justice.
"We did not do that on Friday and it is vital we do in the return."