To make a coffee beverage in a coffee percolator, hot water is fed, at relatively low pressure of about two atmospheres, into a sealed capsule defined by a cup-shaped body housing a measure of ground coffee and closed in fluidtight manner at an open end by a sealing wall connected integrally to the cup-shaped body; the beverage being extracted from the sealed capsule through hollow extraction needles, which have longitudinal inlet slits of substantially 0.3 mm in width, and are inserted into the sealed capsule through the sealing wall before the hot water is fed into the sealed capsule, and so that the relative longitudinal slits extend inside the sealed capsule by respective lengths at least equal to a third of the depth of the relative cup-shaped body.