"There's no place for that in the game,'' Goodell told Gary Myers on the "Pre-Flight Playbook." "He will not play the rest of the season. He will probably meet with us sometime in the offseason, and I think we'll make a judgment on does he have remorse?
"Does he understand why it's not acceptable? Do we understand what he's going to do to make sure it doesn't happen again? Those are the things that are going to be very important for us."
Garrett will miss at least the rest of the season and any potential playoff games for removing Pittsburgh Steelers quarterback Mason Rudolph's helmet and hitting him in the head with it during the closing moments of Thursday night's game.
The star defender appealed the ruling, and the final verdict will reportedly be handed out no later than Wednesday.
"It's probably the most significant discipline we've had from any single incident in our history, although we don't keep that stat, but I'd be surprised if it wasn't," Goodell said. "It was in my view and I think our football people (saw) something that had to be dealt with very quickly and very firmly to make it clear to the players that it's not acceptable."
Browns head coach Freddie Kitchens said Monday that the 23-year-old is a "good person" and his teammates will "continue to support him."