ERJ-170 flight crew reported loss of aircraft control during gate arrival procedure when the parking brake was thought to be set but was not.

Narrative

On Day 0 I was operating flight XXXX from ZZZ1 to ZZZ on Aircraft X as Captain. Upon landing at ZZZ; runway XX exited taxiway 1 and proceeded to the gate. We were guided into the gate and received the hand signal to stop. Both engines were still running due to not having the cool down time. I honestly believe I pulled the parking brake; as I have done on every flight that I have operated. At this point I released the brakes on rudders and was going to shut down the engines when I realized the aircraft was rolling forward. At this point I immediately applied the rudder brakes and reengaged the parking brake. I opened the cockpit window and communicated with the ground personnel to verify the aircraft did not strike the Jet Bridge. Once this was confirmed; the aircraft was connected to the tow vehicle and pushed back to its proper spot. The Jet Bridge was attached to the aircraft and passengers were deplaned.Cause: Parking brake did not engageSuggestions: Ensure parking brake is fully engaged and emergency parking brake light on is illuminated