Ian Madigan did the damage for Leinster, kicking 17 points, while prop Jack McGrath secured their only try while two Lewis Robling penalties and late scores from Dan Lydiate and Will Harries gave the Rodney Parade faithful something to cheer about, despite seeing their side lose a third straight game at home.
Leinster were already guaranteed to finish top and will face Glasgow in their semi-final while the Dragons ended the season ninth but 14 points lower than the closest other Welsh side, Cardiff Blues.
But Charteris, who is heading to the continent next season, believes the Dragons will be a force to be reckoned with in the years to come.
Charteris said: "I think we'll all see that next year the Dragons won't be the fourth Welsh team. They might not win the league, but they can have the beating of the other Welsh teams and have a say in the play-offs at the end of the season.
"The realistic target is qualification for the Heineken Cup.
"It's going to be a lot tighter next season with the salary cap coming in.
"We have a lot of young 17 and 18-year-olds who will have a proper pre-season and there are a few others apart from Jack Dixon and Hallam Amos who could come in and do a job. We can let them loose and you will see a huge difference."
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