Holmgren said Rogers, who was arrested and charged with carrying a concealed weapon through security at Cleveland's Hopkins International Airport on April 1, didn't realize he had a loaded handgun in his carry-on luggage when he was stopped.
Rogers pleaded not guilty to the charge, which carries a maximum penalty of 18 months in prison.
Holmgren said Rogers conveyed his remorse about the arrest.
"He felt bad about it," Holmgren said, according to a transcript posted on the Cleveland Plain Dealer's Web site. "It was not an intentional thing. All of the things that you have written and read about, he made a mistake. Clearly, he made a mistake, but we will deal with those decisions at some point in the future."
Holmgren also said the team will wait before making any decisions about the Pro Bowl lineman's future. Rogers likely will face league discipline for violating the NFL's player-conduct policy.
The Associated Press contributed to this report.