In an inertial frame of reference, an object at rest will remain at rest, and an object in motion will continue moving at a constant velocity unless acted upon by an unbalanced force. In the case of an object placed in air unsupported, the force of gravity is pulling the object downward. There is no other unbalanced force acting on the object, so it will fall downward.

The fact that the room is moving upward is irrelevant. The object is not moving relative to the room, so it will not experience any additional force due to the room's motion.