In one aspect, a bracket for evacuating a storage bag having a one-way valve element is provided that has parallel first and second flat panels that delineate a gap. A bag can be placed into the gap such that the valve element on the bag aligns with an aperture disposed through the first panel. To evacuate the bag, a nozzle of an evacuation device can be inserted through the aperture and pressed against the bag sidewall about the valve element. When the evacuation device is activated, the sidewall of the bag is pulled against the rim of the nozzle and air is drawn through the valve element. In another embodiment, the nozzle can be pressed against the first panel around the aperture. In another aspect, the bracket can be included as part of a handheld evacuation device.