Coach Mike Mularkey said Cox simply was not consistent enough and the Titans need better play at the position.
"If you don't perform at the level that we ask, then we are going to find someone who does," he said.
"... You've got to do it how we would like it, and sometimes that wasn't always the case and sometimes that's just lack of confidence in trusting the system. You've got to trust what we're telling you, and that's what we want."
Cox started nine games this season and 22 in his two seasons with the team. He leads the Titans with three interceptions this season, but he has struggled in pass coverage. Former general manager Ruston Webster signed him as a free agent in 2015.
On Sunday, Cox fell and left Joshua Bellamy wide open in the end zone during the Bears' final charge. Bellamy dropped an easy touchdown.
"I slipped," Cox said. "I looked up and had the ball bouncing right in front of me, happy that the Lord was working on my side on that one and we came up with the next play."
All of Tennessee's cornerbacks struggled against the Bears, as Matt Barkley threw for 316 yards, three touchdowns and two interceptions.
The Titans promoted rookie Kalan Reed, who was the last pick in the draft, from the practice squad to fill Cox's roster spot.
The 6-6 Titans have a bye Dec. 4 and return to action Dec. 11, when they host the Denver Broncos.