Parker assisted Chiefs' opening goal as the AmaKhosi went on to claim a 2-1 victory over the Buccaneers at Orlando Stadium on Saturday afternoon.
The 35-year old had to play different positions after Amakhosi were forced to make substitutions due to injuries, but he dedicated the win to the supporters.
"It was a big victory, the lads knew that this game is very important for us to gain momentum and to make sure that every game come across we get the three points," Parker said on SuperSport TV.
"It was good motivation booster for the team, well done to lads, we had the plan, we stuck to the plan and executed. It's just that we allowed them back into the game.
"We started giving them space, which our plan was to deny them space but we let them come in, open up the field which what Pirates want when they change play," he said.
"But we kept it tight it's just the little error where they caught us on a counter, it's a mistake, we learn from our mistakes. It's just for us to keep calm, we need to refocus and not celebrate too much.
"This derby was for the fans, we missed you guys so dearly, we really missed you and we hope to see you soon."