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."
Wales Head Coach Rob Howley talks to WRU TV's Sebastian Barrett about the 36-man squad he has just named for the forthcoming Under Armour series, which includes two uncapped players, Ospreys duo Sam Davies and Rory Thornton.
Head coach Rowland Phillips is deligthed he can now call BT Sport Cardiff Arms Park home for his Wales Women's side, who launch their international season next month with games against Scotland and UK Armed Forces in the heart of the capital city.
Wales Sevens star Sam Cross has put his home town club of Brynmawr on the map after winning a silver medal at the Rio Olympics with Team GB. His club have now honoured him by naming their players bar after him, as WRU TV discovered at the official launch, recently.
One of the newest members of the Principality Premiership, Bargoed admit it's proving to be a steep learning curve at the highest level, but are determined to become a force to be reckoned with. WRU TV visited the club last weekend when they took on Llanelli.
Table-topping Aberavon travel to north Wales to tackle RGC 1404 as both teams defend unbeaten starts to the season in the Principality Premiership. WRU TV's Graeme Gillespie visited the Wizards to see how their preparations were going for the game of the weekend.
The Half a Game initiative is currently sweeping across Wales and proving a major success. The scheme aims to give every young player at least half a game every weekend. WRU TV recently visited a festival in Narberth where clubs have fully embraced the initiative.
Both Bargoed and Swansea were seeking their first win of the Principality Premiership season this afternoon. It proved a fruitful day for the hosts - not only did they win, but Bargoed claimed a try bonus point.