EMB-175 First Officer reported the aircraft rolled back a few feet after parking at the gate when the Captain apparently failed to set the parking brake.

Narrative

At the completion of Flight ABCD; we pulled into the gate and had both engines shut down when the aircraft began to roll backwards 2-4 feet. I immediately noticed movement from outside of the aircraft; but just assumed it was the jet bridge that was moving toward the aircraft. After about a half second I noticed that the illusion I was facing could not have been the jet bridge moving at the speed that I saw. I then felt a sensation that the aircraft was possibly moving. Which was confirmed to me by looking at other visual cues outside of the aircraft. As I began to depress the toe brakes I simultaneously quarried the Captain about the movement of the aircraft; who had already began to smoothly apply his toe brakes. After the aircraft was stopped we both noticed and confirmed; via the parking brake light; and the lever being in the down position; that the parking brake was not engaged. The Captain set the parking brake and called for the shutdown checklist. Ground personnel retrieved a tug and then pulled us forward to the correct parking position. Cause: The parking brake was not set after arriving to the gate which allowed the aircraft to roll backwards after arriving to the gate. Suggestions: I am almost positive that the parking brake was not set after parking at the gate. Going forward I will now monitor the Captain's actions as they do their flow and monitor the aircraft's response to those inputs. I should've been doing that all along; but with me being fairly new to this equipment; I try to focus on following my own procedures outlined in the company AOM to make sure the aircraft is properly set up for that phase of flight.