In a 30-minute Tuesday afternoon interview with KRLD-FM Dallas/Fort Worth, Jones also said there are some highly-priced contracts the team shouldn't have completed and believes the franchise would have won more titles if not for the current financial system in the NFL.
"We should have been knocking on the door and we haven't and I have no excuses, it starts here," Jones said. "But we have not. I know that to the extent that we have a healthy Romo, our best chance to get back to the Super Bowl is a healthy Romo."
The Cowboys have won just one playoff game with Romo as quarterback, 2009, and missed the postseason the last four seasons.
In the last three seasons, the Cowboys had a chance to reach the postseason by winning the NFC East in the regular season finale but lost each time.
Several years ago, Jones said he conferred with several former or current NFL personnel executives who advised from 2007 to 2010, the Cowboys had some of the best talent in the league. During that time, the Cowboys not only had Romo, but Pro Bowl players such as Terrell Owens, Flozell Adams, Jason Witten, Roy Williams, Marion Barber, DeMarcus Ware and Miles Austin.
Yet, the Cowboys could only manage one playoff win and advanced to the NFC divisional round twice, losing both times. After a first-round bye, the Cowboys were beaten at home by the New York Giants in 2007 and then the Minnesota Vikings in 2009.
Since 1997, the Cowboys have compiled a 136-136 mark.
"Now for us not to having got it done during those years is a mess up," Jones said. "You got to get it when you're high like that. When you're high up on it. You can't miss your bus when you got your quarterback and you got good talent around him and if you miss that bus in the NFL."
Currently, the Cowboys are estimated to be $20 million over the projected $130 million salary cap for the 2014 season. The Cowboys, like most NFL teams, need to get under the cap by March 11.
The Cowboys can create $17 million in cap space with the restructured contracts of linebacker Sean Lee, cornerback Orlando Scandrick and Romo. The team is also thinking of restructuring Ware's deal. If the Cowboys release Ware, it opens up $7.5 million in cap space.
"All of that boils down to management of a cap, management of certainly having players that deserve to get the money that you got," Jones said. "When I look back on it, we probably paid some people that we probably would have been better off not paying."