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."
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