A321 flight crew reported aircraft loss of control during parking procedure at gate.

Narrative

Arriving at gate XX at ZZZ Airport I was guided into the gate with two wing walkers and a parking guide person. I was on the line and stopped the aircraft in the designated spot. My hand was on the parking brake and I applied brakes with my feet. I then went to set the parking brake thinking the parking brake was set. I looked down to shut the engines off when I looked up and noticed the plane was slowly rolling forward; and the guide person was signaling to apply brakes. I immediately applied brakes and reset the parking brake. The aircraft was stopped and we had to be towed back into position. I reapplied the brakes and we parked uneventfully.Cause: I believe causal factors in this event was when I set the parking brake I did not visually verify the triple indicator showing the brakes were actually set; and I thought that my actions with my hand on the brake handle set the brakes. I believe that the parking brake handle which needs to be fully moved Clockwise to the on position did not go into position and when I released my hand the break Was off. It is important to visually verify the position of the parking brake handled is in the on position and that the triple indicator shows brake pressure.