Three defeats have left the Dragons stranded in the basement of the group with just one losing bonus point to show for their efforts.
But coach Paul Turner has vowed that his team will "still have a say in the outcome of the Pool" despite suffering that hat-trick of reverses.
The Dragons have tough away games at Munster this weekend and Pool leaders Sale Sharks in Round 4 to come, as well as a home clash with Castres Olympique in Round 6, but Turner claims his side will not be throwing in the towel.
"We are certainly going to be looking forward to visiting Thomond Park on Saturday. It is a great place to play, even if it promises to be a steep learning curve for a lot of the club players who have had to play their part in the tournament because of our injuries.
"We are trying to develop our youngsters and I was delighted with the way everyone stuck at it against Munster.
"Sale's win in Castres was a tremendous performance, even though the game could have gone either way. They did well up front and they nullified the Castres scrum and tied in their All Black props.
"Charlie Hodgson did the right things at the right time and they are really on a high now. I am sure Sale and Munster will be around the top of the group but we still feel we can make a contribution to the final outcome.
"Munster were a bit too street-wise for us in the contact area and we made a lot of basic errors. But I was proud of the way we competed and stuck at it. We have got a small squad and we have been hit by some significant injuries to players like Hal Luscombe, Kevin Morgan, Nathan Brew, Gareth Wyatt and Jason Forster."
Ahead of their SSE SWALEC Bowl Final clash with Taffs Well at Principality Stadium on Sunday, Burry Port share their #FABXV nomination with WRUTV in the search for Welsh rugby's greatest volunteers. Everyone can get involved by sending nominations via twitter to @WRU_Community using the hashtag #FABXV
Cardiff Blues prop Gethin Jenkins and Ospreys centre Ben John look ahead to the first game at Principality Stadium in Saturday's double header which is promising to be a special occasion for all Welsh fans.
Carmarthen Quins Director of Rugby Ian Jones and committee member Jeff Thomas along with Llandovery chairman Handel Davies look ahead to Sunday's SSE SWALEC Cup showdown where both teams are out to prove 'West is best'
SWALEC ambassador Shane WIlliams is looking forward to Sunday's Finals Day where the Cup, Bowl and Plate offers a great opportunity for players and teams to experience the magic of playing at Principality Stadium
Carmarthen Quins coach Richard Kelly believes it is an exciting time to be part of the Scarlets region as his side take on local rivals Llandovery in the SSE Swalec Cup final on Sunday, as WRU TV's Graeme Gillespie discovers
Scarlets long serving prop Phil John talks to WRU TV's Graeme Gillespie about Judgement Day IV and SSE Swalec Cup finals day. The last time Llandovery were in the cup final in 2007, the Drovers claimed the spoils with Phil playing a major role in the engine room.
Meet Aberdare coach Luke Thomas whose #FABXV nomination goes to super volunteer Daz with a whopping 10 things he does for the club each week, all except the ironing! You can also join in the search for Welsh rugby's greatest volunteers, by sending your nomination via twitter to @WRU_Community using the hashtag #FABXV
SSE Swalec Cup kings Pontypridd travelled to Swansea, fully expecting a return to their second home but Llandovery had other ideas as they also sought victory in the semi-final to earn the right to play the final at Principality Stadium