The south-east Wales side have failed to finish above compatriots Ospreys, Scarlets and Cardiff Blues in the PRO12 in each of the last 11 seasons.
But, ahead of Saturday's season opener against Connacht Rugby, Jones wants his team to hit the ground running and prove they finally have what it takes to end the season as the highest placed Welsh region.
"The Ospreys have been the leading light in Welsh rugby for too long. They need to be challenged and it's up to us, Cardiff Blues and the Scarlets to pick it up and surpass them," Jones told the South Wales Argus.
"In the Celtic League there's one side from Scotland that's very strong - Glasgow - three from Ireland (Leinster, Ulster and Munster) and all the Welsh regions are nip and tuck, so there's lots to play for.
"I think that the Blues have signed well. Wayne Pivac [head coach] will give the Scarlets an edge and has a huge reputation in New Zealand, while the Ospreys have always had high standards."
The Dragons have had a busy summer with ten new faces coming through the doors at Rodney Parade.
Lee Byrne and Aled Brew head the recruitment drive following their respective arrivals from Top 14 clubs Clermont Auvergne and Biarritz Olympique.
And Jones feels if he can keep the core of his squad injury-free throughout the season, they can achieve their goal of a strong domestic finish to propel themselves into the European Rugby Champions Cup.
"It's difficult to see who will finish where but the key to it all is injuries," he added. "If you've got your best players on the field for most of the season you are going to do well.
"The squad is the key because everybody will get injured from time to time, but the people coming in need to be of equal ability and hungry."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland