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."
Meet the members of the WRU's inaugural Youth Board - after an online selection process which saw a host of high calibre candidates submit video applications the WRU has made its first 15 appointments.The board is made up of individuals aged between 16 and 21, and will meet for the first time at Principality Stadium on Monday 15th February.
The Wales Women's team headed to Dare Valley Country Park on a team bonding exercise as the entire squad got together for the very first time in preparation for this season's Six Nations championship which kicks off on Saturday with a clash against defending champions Ireland, in Donnybrook.
Wales Head Coach Warren Gatland discusses his team selection for the opening round of the RBS 6 Nations where he leads his side against Ireland, on Sunday. As WRU TV's Luke Brodley discovers, Gatland is fully aware of the challenges the defending champions pose
WRUTV caught up with Wales Women captain Rachel Taylor at the RBS 6 Nations launch and how a good crowd really helps boost the girls performance. Tickets for all three Women's home games at The Gnoll, Neath are available from www.wru.wales/tickets