It marked the second time this season that Cunningham didn't play due to a violation of team rules. He was benched for the first quarter of the Texans' Week 2 matchup against the Cleveland Browns for recurring tardiness.
"We've got standards. Didn't feel like those standards had been met consistently," Culley told reporters. "And I feel like I made a decision that was the best for our team. This is about the team, it's not about any individuals."
Culley noted that the decision to move on from Cunningham "wasn't tough at all."
"It's about the team, it's not about any individual player," he said. "And one thing that we always talk about is that it's not necessarily trying to be the best player on the team, but being the best player for the team. And that's our motto."
Cunningham, who was a second-round pick in the 2017 NFL Draft, signed a four-year, $58 million contract extension with the Texans in 2020. The linebacker compiled 67 total tackles, one forced fumble and three passes defensed over 10 games for Houston this season.
The Texans explored trade options involving Cunningham during training camp and before the deadline, but the team wasn't able to find a suitor.
The move to cut Cunningham will leave the Texans with $5.5 million in dead money this year and $12.8 million in 2022.