Coach Mike Smith ruled both starters out following a joint practice Wednesday night between the Falcons and Jaguars.
Robinson is dealing with a hamstring injury, and Smith says McClure is just getting extra rest. Linebacker Robert James has a groin injury and his playing status will be determined before Friday's game.
Defensive end Ray Edwards, one of the team's top free agent acquisitions, practiced in a limited role Wednesday and could make his Falcons debut Friday. He also will be a game-time decision.
Defensive tackle Corey Peters already has been ruled out because of a knee injury.