The assembly for use in a coffee machine comprises a container having a bowl-shaped inner space bounded by a bottom having at least one outlet opening and at least one vertical sidewall. The assembly further comprises a pill-shaped pouch manufactured from filtering paper and filled with ground coffee, accommodated in the inner space of the container. The pouch extends over the bottom to a position adjacent the vertical sidewall. In the bottom, a number of channel-shaped grooves are provided, extending in radial direction of the container to the outlet opening. The grooves extend from a position located at a distance from the sidewall in the direction of the outlet opening. This prevents bypass.