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The Irish province may sit four places above the Llanelli outfit in the GUINNESS PRO12, but that will count for nothing at the Kingspan Stadium on Saturday after Ulster lost their opening two European encounters against Leicester Tigers and Toulon.
Neil Doak's side now face an uphill struggle to make the quarter-finals for the fifth season in succession, with no side ever making it out of the group stage of the top-tier of European competition having lost their first two matches.
But with three best placed runners-up going through this year, a defiant Bowe believes Ulster still have it in them.
"I suppose being written off is nice motivation for us," said the 30-year-old wing. "But there is no dismissing the next two matches. We know not winning our last two has made things incredibly difficult for ourselves.
"Everyone says we have to hit 20 points to qualify from the group, but this year I think there are going to be a few teams who don't quite make that target and still get through.
"We are still there, but we have a massive task ahead. I suppose we first have to get the two wins against the Scarlets, getting bonus points if we can.
"Certainly at home this Saturday we would love to pick up maximum points. But that can't be on our minds at the outset, we will just be going out there to get the win.
"The Scarlets will be pretty fired up and looking forward to this match as well. They've beaten Leicester and put up a great fight away to Toulon, so it is not going to be an easy match.
"But we're massively excited about the next two weeks. As a team we know how good we are - as a collective and as individuals - and come a big European night we need to pull it out."
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Neil Doak's side now face an uphill struggle to make the quarter-finals for the fifth season in succession, with no side ever making it out of the group stage of the top-tier of European competition having lost their first two matches.
But with three best placed runners-up going through this year, a defiant Bowe believes Ulster still have it in them.
"I suppose being written off is nice motivation for us," said the 30-year-old wing. "But there is no dismissing the next two matches. We know not winning our last two has made things incredibly difficult for ourselves.
"Everyone says we have to hit 20 points to qualify from the group, but this year I think there are going to be a few teams who don't quite make that target and still get through.
"We are still there, but we have a massive task ahead. I suppose we first have to get the two wins against the Scarlets, getting bonus points if we can.
"Certainly at home this Saturday we would love to pick up maximum points. But that can't be on our minds at the outset, we will just be going out there to get the win.
"The Scarlets will be pretty fired up and looking forward to this match as well. They've beaten Leicester and put up a great fight away to Toulon, so it is not going to be an easy match.
"But we're massively excited about the next two weeks. As a team we know how good we are - as a collective and as individuals - and come a big European night we need to pull it out."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12
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