Romo, 34, led the Cowboys to a come-from-behind 31-28 win over the New York Giants on Sunday to improve to 8-3 on the season.
Jones said it will be a huge disappointment if the team doesn't win a Super Bowl during Romo's career.
“It will be the most negative thing about my ownership if Tony [Romo] has a career here and we don’t win a Super Bowl,” Jones said.
Earlier this month, Cowboys executive vice president Stephen Jones said it would be the family's fault for not giving him better teammates if Romo never wins a Super Bowl.
The starting quarterback since six games into the 2006 season, Romo is a three-time Pro Bowl quarterback who has put up some gaudy stats -- he is fewer than 900 yards away from passing Troy Aikman as the most prolific quarterback in franchise history. His 96.9 passer rating is the best in Dallas history, as are his 230 touchdown passes and 64.9 completion percentage.
Romo has started just four playoff games in his career, and the Cowboys are 1-3 in those games. Dallas hasn’t been to the postseason since 2009, but is in position to end that streak this season.
This season, Romo has started 10 games -- he missed Dallas’ Nov. 2 loss to the Arizona Cardinals with a back injury -- and has completed 68.8 percent of his throws for 2,519 yards and 22 touchdowns, with just six interceptions. His 111.4 passer rating is a career best, as is his 8.5 yards per attempt.
Dallas is tied for first place in the NFC East with the Philadelphia Eagles. The teams will play on Thanksgiving in Arlington, Texas, with the division lead on the line.