Air carrier flight crew reported aircraft movement while parked at the gate due to parking brake not set.

Narrative

During parking at Gate X at ZZZ the captain neglected to set the parking brake. The aircraft rolled backward; away from the gate approximately XX ft. The captain noticed this and applied the parking brake to stop the movement. I was completing my parking flow when I felt the aircraft move slightly. This motion was the result of the parking brake application. I did not notice the initial backward motion as it was slight and linear and I was focused on shutting down fuel pumps. The aircraft came to a stop. We checked with the flight attendants and ground crew. No injuries or disturbances of any kind were reported. We prepared the aircraft to be towed back to the parking line. We parked and completed the parking checklist. There was heavy rain at ZZZ. The visibility was low and the wipers were in use when we were parking. I believe shutting off the wipers interrupted the captain's parking flow and led to the omission. Anyone could've done it. Preventative measures are adherence to company procedures.