Parker scooped up the Man of the Match award as Chiefs defeated the Citizens to advance to the Nedbank Cup last four.
"Firstly, I would like to thank the fans for coming out here in numbers," Parker told SuperSport TV.
"I'm sure that everybody from all across the country, from every corner is here today. I would like to thank them for the support and the support from the Kaizer Chiefs family and the support staff."
"It's unbelievable what we did here today.
"We managed the game well. We kept them on the backfoot. We got a few chances. We could have got more goals. But the good thing is that we got goals and we got the result.
"I know the coach is not completely happy. He knows we can do better. But we can improve from here. We can take all the positives from today and put it in our back pocket and correct our mistakes. From there we can go on. This is the kind of spirit, the Kaizer Chiefs culture that the supporters need to see week in and week out."