After four games, Warriors sit bottom of Pool Four with just two bonus points to show after losses to Ulster and Northampton as well as a double-dunt against French cracks Castres.
Yet, while Glasgow's hopes of making it through to the knockout stages for the first time were left shredded as early as their home loss to the Northern Irishmen in the opening section of the group campaign, these results have not told the whole story of their Euro journey this term.
In their opening loss at Northampton, Warriors played the Saints off the park for 35 minutes before a succession of backline injuries decimated their line-up.
At home to Ulster it was a tale of missed kicks that cost Gregor Townsend's side dear.
Although the home loss to Castres may have been unacceptable, Warriors fronted up manfully on French soil and only the woodwork stopped Ruaridh Jackson kicking them to a famous victory at the Stade Pierre Antoine.
Murchie said: "There is a lot of frustration within the squad as we set out with high hopes and great expectations.
"However, we have not managed to deliver on them. At the same time we are better than our results have indicated and beating Ulster on their turf is the best way to underline that.
"There is very much a case for saying that our pride is on the line. There is no way we want to go through this campaign without a win but we are not looking at it like that.
"If we can beat Ulster then we can turn around into our final pool game at home to Northampton tomorrow week with massive momentum and hopefully go out on a high with our pride restored."
HE ADDED: "Tonight's game is the first up of all the ties on the Sky coverage so we have the platform to show just what Glasgow Warriors can do when we fire on all cylinders.
"But it will take an 80-minute performance and that is exactly what we have failed to produce in Europe this season."
Warriors head coach Townsend has made six changes from the starting side which hammered Treviso at Scotstoun last Friday in PRO12 action.
Duncan Weir replaces Jackson at stand-off while Peter Horne returns at inside centre.
Alex Dunbar keeps his spot at outside-centre with Murchie taking up the full-back slot.
Sean Maitland returns in place of Tommy Seymour, with DTH van der Merwe on the opposite wing.
Tom Ryder starts at lock while James Eddie returns in the back row.
But Murchie admitted: "For me this one against Ulster will be won by our ability to stop their ball carriers and get ours going."
Glasgow: Murchie; Maitland, Dunbar, Horne, van der Merwe; Weir, Pyrgos; Grant, Hall, Low, Ryder, Kellock, Eddie, Harley, Strauss.