EMB-175 Captain reported a failure to ensure the parking brake was set correctly resulted in the aircraft rolling backward until stopped with the normal brake application. There were no injuries or damage reported.

Narrative

Arriving at the gate; the parking brake was not set properly because I may have knocked it off or not properly set it without realizing it. I am honestly not sure. The aircraft rolled backward 5-10 ft.; (according to ground crew); until I reapplied the parking brake to bring the aircraft to a stop. The stop was abrupt; but I spoke immediately with both flight attendants and neither of them said that they were hurt. The flight attendants also had checked in with the passengers who were standing up in the aisle. They said that no one had fallen or reported being hurt. After this; I contacted Operations to make sure that no one was hurt and that everything was ok on the ground. They said everyone was fine and that nothing other than the aircraft movement had happened. The entire event happened in a matter of seconds.The parking brake not being engaged caused the aircraft to roll backward. Completing the engine shut down flow contributed to me not catching this immediately (although I did catch it with in a matter of seconds).Making sure the aircraft is totally secure is the most important task of the engine shutdown flow. Setting the brake on the engine shutdown flow is the first thing to do and I find it hard to believe that I would have missed it. Regardless; I plan to initiate a new personal check by calling out; parking brake set and by visually verifying it a second time after my flow is complete.