They started that attempted surge up the domestic rankings in style with a home victory over Ulster and Coombs is keen to see the Dragons make it two wins from two at Edinburgh on Friday.
"There's no getting away from the fact that we've underachieved as a region for the last few seasons," said Coombs.
"That's something that everyone wants to put right. It doesn't matter who you are - player, coach or kitman - we're all working hard to make the Dragons something special.
"Last season we probably deserved to come last of the Welsh regions but in the seasons before that when the likes of Luke Charteris and Aled Brew were playing for us we were very competitive. It's important that we get back to that strength and finish as at least the third best Welsh region this year - that's the minimum goal."
The man charged with heading that quest for improvement is former Ospreys boss Lyn Jones, who joined the region as director of rugby after a hugely successful spell with London Welsh.
Coombs insists the new boss has already had a major impact on everyone involved with the Dragons, both in terms of what's being achieved on the training field and in creating an increased positivity and confidence throughout the squad.
"Lyn is a proven, quality coach who's achieved so much in his career. Just having his experience around Rodney Parade is great for our players," added Coombs, whose men head to Scotland in search of back-to-back wins having not achieved that feat at all in the league last term.
"We're learning so much in every session with him. He puts so much detail into the game and you can see how much the boys are developing week-on-week from spending time with him on the training field.
"Self-confidence is something that Lyn's really installed in us. He's shown us how much we've come on over the last few months. We've looked at where we were when he came in and where we are now and the progress has been really good. With a few more months under Lyn, I'm sure we'll be a really strong team.
"There's a real buzz here at the moment. You look at the media and see that the Dragons are highly talked about. Where I'm from up in Nelson you very rarely hear the Dragons talked about but, right now, we're the region that's being talked about the most. It's the first time in a long time that the Dragons have been spoken about in this way and we just want to keep that going now."