A gastight interface for an evacuation device includes a flexible suction cup adapted to form a gastight seal with a surface surrounding a valve disposed on a container and extending from an evacuation end of an evacuation chamber. The flexible suction cup has an aperture disposed therethrough for fluid communication with the evacuation chamber. A plurality of support members extends from the evacuation end of the evacuation chamber to restrict movement of the flexible suction cup between the surface and the evacuation end of the evacuation chamber, to allow fluid communication between an interior of the container and the evacuation chamber through the valve when the valve is in an open position, while the piston is being reciprocated between the closed end and the evacuation end. Each support member has a distal surface disposed outside of an outer perimeter of the flexible suction cup.