When in use, the sealed cartridge (1) containing a certain amount of a substance intended for the preparation of a bewerage by dissolution or extraction with a liquid, is placed inside a liquid collector member comprised of a frusto-conical beaker (9). The assembly thus formed is placed inside a housing (21) of a "spoon" of a coffee machine. The top of the cartridge (1) is perforated by a perforator and injector member which injects a liquid under pressure inside the cartridge (1). The lower membrane (2) of the cartridge undergoes a deformation under the effect of the pressure thus generated and is pressed against perforator tips (13) at the bottom of the beaker (9). The liquid flows into the housing (21) and can be collected in cups. The invention makes it possible to optimize the contact time of the substance contained inside the cartridge with the liquid supplied for its dissolution or its extraction.