The 29-year-old receiver, whose contract expires in March, discussed his pending free agency Tuesday on Twitter and said, "Honestly, the front office pushes who they want to get the ball to. I haven't been a huge priority in that regard."
Jones addressed Beasley's comments Wednesday on "The Rich Eisen Show."
"I would hope that's just his frustration but (it's) certainly not at all the case," Jones said, according to NFL.com's Kevin Patra. "We don't get involved in that. The only thing we ever do is decide if we're going to pay players a lot of money. Or if we're going to trade for players and give up big picks. We certainly hope that they would be involved if we're going to do things like that. ...
"But we would never dictate where balls go or things of that nature, in terms of the game plan and getting involved with what our coaching does to get ready to play the ballgame. And certainly of all people, Cole is always involved in getting balls and getting catches. He's been just an integral part of what we're about. Certainly, he's made a lot of big catches and key catches in games that we've won."
Beasley finished the 2018 season with 65 receptions, 672 receiving yards, and three touchdown catches. His 87 targets were second on the team.
However, his targets did drop from an average of 6.14 per game to 4.45 per game after the Cowboys acquired Amari Cooper from the Oakland Raiders, Patra notes.
On Wednesday, Beasley said he hadn't intended to criticize the Cowboys in particular. "EVERY team's game plan in pro sports is dictated by the front office," he tweeted. "Big free-agent additions, high draft picks, etc. are going to get the most (opportunities). And I'm not mad at that!"