But with plenty of pride still to play for, Gavin Duffy, the Connacht captain, has called for his side to deliver victory against the English aristocrats to ensure they end their debut Heineken Cup campaign on a high.
"Everyone in the squad is looking forward to the match this Friday," said Duffy, who was a Harlequins player earlier in his career.
"We know the result didn't go our way last weekend even though our performance was much improved on the week before and after two weeks on the road everyone is itching to get back out in front of our home support and show we're in this competition for a reason."
Eric Elwood, the Connacht coach, has admitted it has been a baptism of fire for the Irish province and he has been disappointed by the five defeats in the Pool stages but believes the experience has been invaluable for his team.
"As Munster and Leinster fans have reminded us throughout the course of this journey, the Heineken Cup is a not a forgiving environment and both teams experienced rough rides in their early years in the tournament," said Elwood.
"Aside from the first 40 minutes against Toulouse at home, every team we've played has known they've been in a battle with us and the margins have been tight.
"Connacht fans have gained the respect of our European counterparts and Friday represents a final opportunity to show all of Europe the passion and rugby knowledge that exists across the province."
Elwood has admitted his side are willing to answer Ireland's call and put their bodies on the line against Harlequins to get a victory that would guarantee a third quarter-final slot for Ulster ahead of their journey to ASM Clermont Auvergne.
"At this stage of the season, we are not afraid to admit that we are up against it in terms of qualification for next seasons Heineken Cup," said Elwood.
"That doesn't mean we'll stop trying and our supporters are assured we'll fight to the very end of the Rabodirect Pro12 but, as of now, this could be our last Heineken Cup match for a while and that gives us huge motivation to go out and get that performance and result."