The Texans reportedly shopped Jones to other teams after selecting Ohio State wide receiver DeVier Posey on Friday in the third round of the 2012 NFL Draft. The team took another wide receiver, Michigan State's Keshawn Martin, in the fourth round Saturday, further making Jones expendable.
"We've got a couple of kids that we think a lot of ... and then also a lot of it's about doing right (by) Jacoby -- our football team but doing right by him, too," Texans coach Gary Kubiak said Tuesday, according to the team's official website. "(General manager) Rick (Smith) and I talked about it, and he's handled himself with class."
Jones was scheduled to make $3 million next season, the second year in a three-year contract. He had been with the Texans since they drafted him in the third round in 2007, and he had his best season in 2010, when he caught 51 passes for 562 yards and three touchdowns.
But Jones caught just 31 passes for 512 yards last season, while star receiver Andre Johnson spent much of the year recovering from injuries. Jones also drew Texans fans' ire after muffing a first-quarter punt against the Baltimore Ravens in an AFC divisional playoff game that Houston lost.
"I think there's way too much made out of that," Kubiak said. "Andre missed 10 games last year, and Jacoby was a starter in his absence and made a lot of plays for us, and Jacoby made a lot of special-teams plays. We had many opportunities to win in Baltimore, and in this business, not one guy loses the game, not one guy wins the game."
Jones averaged 10.2 yards on 179 career punt returns for the Texans and scored three touchdowns. He also scored a TD on a kickoff return.
"We had a few rough patches early in his career with me, but he's really grown up and done a good job," Kubiak said. "To me, he's been excellent the last couple of years. ...
"We'll move forward with our young players at receiver, and it's a fair opportunity for Jacoby to go out there and get a fresh start somewhere else, and I'm sure he'll go out and go a great job. I appreciate everything he did. Visited with him today, I wished him all the best and thanked him for everything he did for us."
The Associated Press contributed to this report.