Smith was suspended Wednesday for the last two preseason games and Houston's season opener for hitting Miami guard Richie Incognito with the Dolphins player's helmet.
Smith appealed the suspension, but his appeal was denied Friday.
Kubiak says he's disappointed in the decision, but that the team understands and accepts it.
Smith ripped the helmet off Incognito's head, then hit Incognito on the shoulder with it Saturday night in the teams' preseason game. The two also went at it in last season's opener, when Smith kicked Incognito, drawing an $11,000 fine. Smith later said Incognito deliberately tried to twist his ankle while holding his legs in the 2012 game.