Warriors were beaten 9-6 by the French Top 14 side at Scotstoun on Friday night and the try-less fixture killed off Warriors' Euro hopes before Christmas for yet another year.
But now Murchie wants the Glasgow side to use the pain of that loss to help sign off from European action with a win and provide a helping springboard into the 1872 Cup double-header with Edinburgh.
The Warriors full-back said: "There will certainly be a fear factor about going to Castres and that is because if we don't dramatically improve from the first game then we could take a sore one.
"What Sunday afternoon is all about is getting our season back on track. We know that the Scotstoun performance was just not good enough, we have to show more pride in the jersey and if we don't Castres will give us a sore one.
"They have played themselves right back into things with their win over us and will know that if they do the double they will have a real chance of going through.
"All of that means that on their home soil they will be 100% focused on doing a job on us. So we are going to have to go over there and give it everything."
Murchie added: "But that is now three defeats in a row and it is vital we put the full stop on that and give ourselves a springboard into the double-header with Edinburgh.
"Europe may be gone but we can't allow how badly it has gone to affect our domestic form.
"We are still sitting fifth in the PRO12, just one place off the play-offs, and that means winning in France is a must if we want to get our confidence back for the Edinburgh games."