Glasgow assistant coach Shade Munro insists the Warriors proved last season that they are a match for any side in Europe.
The men from Firhill defeated European giants Biarritz and Munster last campaign and now Munro wants the side to replicate that form throughout the new term.
The Warriors were within one game of qualifying for the knock-out stages of the European Cup after wins over Biarritz and Viadana before falling at the last hurdle to Saracens at home.
Sean Lineen's outfit finished in their highest ever position in the Celtic League and there success was rewarded with record crowds at Firhill.
Former Scotland man Munro said: "We have definitely improved our credibility in the last three or four years. You have to consistent for people to rate you and we have improved and continued to perform at this level.
"Beating Biarritz at home just before Christmas was massive and so was winning away to Munster in the last game of the Magners League.
"We're playing against the top teams in Europe and we sit among the top five teams in the Celtic League, so we are one of the big teams now and there is nothing for us to fear."
England's preparations for the Autumn International series were potentially dealt a further blow as Maro Itoje was forced to undergo an x-ray after Saracens' European victory over Scarlets on Saturday night.