Jordi Murphy says the Challenge Cup will be "huge" for Ulster after their Guinness PRO14 title hopes were ended by Leinster on Saturday night.
With the northern province having never having competed in European rugby's second-tier competition before, they'll be in the hat for today's last-16 draw having dropped down from the Heineken Champions Cup in this season's altered format.
After what was already an abridged campaign saw the final two rounds of pool action scrapped, EPCR decided to press straight to the knock-outs in both European trophies, with Ulster among the eight teams knocked down from the top table as a result.
When the ping-pong balls are drawn in Switzerland at 12pm, Ulster will be kept away from their seven PRO14 rivals also in the running for the trophy, while they can only face London Irish and Leicester Tigers away from home.
The eight possible opponents include that pair and their English counterparts Newcastle Falcons, Northampton Saints, Bath and Harlequins, and the Top 14 duo of Agen and Montpellier.
While there is certainly a potential for a tough tie, with the current European heavyweights remaining in the Champions Cup, Ulster will look at this as a real opportunity to end a trophy drought that goes all the way back to the 2006 Celtic League title.
"It's huge for us," said Murphy, who has been acting as the side's captain in recent weeks with Iain Henderson away for the Six Nations. "We want to win silverware.
"It's hugely disappointing that we're not going to get the chance to compete for the PRO 14 but the Challenge Cup is still available and the Rainbow Cup, or whatever might come at the end of that.
"We've two more league games (in the PRO14) and we want to put some good stuff out there before that."
The first of those comes against Dragons at Rodney Parade on Saturday evening, with Ulster likely still smarting that the contest has been rendered nothing more than a dead rubber.
While Leinster were always likely to be the Conference A table-toppers come the end of the season, their neighbours to the north had backed themselves to at least keep up the pressure to the end before last week's loss featuring a controversial red card for Andy Warwick.
The hosts' frustration was rooted not in the colour of the card shown to their replacement prop but that Leinster's Jimmy O'Brien had previously escaped the same sanction for a tackle that resulted in contact with Ian Madigan's head.
Murphy admitted that his efforts to seek clarity from referee Frank Murphy ended only in frustration.
"It's difficult because you try to chat to him and try to figure out how one thing is a straight red and one thing, from the rules I know, seems to be a red also (but is given a yellow)," he added.
"That's his job, to make that decision. It's just trying to keep heads high when your backs are against the wall but, look, we've a strong-minded group and I was very proud of the way we bounced back from certain situations. The boys never stopped giving their all.
"We always talk about fighting for every inch and there was definitely times when we did really well in that aspect."
With Jacob Stockdale, Tom O'Toole and Stuart McCloskey all joining back with Ireland this week, Ulster were always going to have to make changes for the trip to Dragons on Saturday, while the physical toll of recent weeks will be considered too.
"We've got a few battered bodies after the weekend," said McFarland.
"There'll be an opportunity for a couple guys to step up who have earned their shot on merit."