Jones didn't provide exact details of negotiations during an appearance on 105.3 The Fan Radio in Dallas, likely in fear of tampering allegations, but he explained the Cowboys' overall mindset.
"The coverage of it has been pretty accurate," he said, per Jon Machota of The Athletic. "We obviously were trying to utilize our (draft picks) to help the Cowboys better than we could've used the same picks in the draft."
Connor Hughes of The Athletic reported Dallas was "very, very much" interested in Adams in the hours leading up to the deadline, but New York sought "a whole lot" in return. The teams clearly weren't able to bridge that gap in time to make a deal Tuesday afternoon.
The situation created a rift between the 2018 Pro Bowl selection and the Jets' front office.
Adams detailed his stance on social media while taking a shot at general manager Joe Douglas:
The Cowboys have been one of the NFL's most balanced teams during the season's first half. They rank first in total offense (437.9 yards per game) and eighth in total defense (324.9 yards allowed per game), which suggests they have more upside than their mediocre 4-3 record may indicate.
One issue has been a lack of game-changing plays on defense. Dallas has forced just nine turnovers through seven games. It also ranks tied for 20th with 17 sacks.
Adams, who's recorded 5.5 sacks, four forced fumbles, three fumble recoveries and two interceptions across 39 NFL appearances, could have filled that defensive game-changer role. He's also racked up 237 total tackles and 23 passes defended since the Jets selected him with the sixth overall pick in the 2017 draft.
Although the Cowboys weren't able to work out a blockbuster deal, they weren't alone as the rumor-filled weeks leading up to the deadline ended with few actual trades.
Dallas may circle back in the offseason to check on Adams' availability, with starting strong safety Jeff Heath set to become an unrestricted free agent after the 2019 campaign.