The Soweto giants are winless at home in the league this season - having registered two defeats and three draws.
Parker discussed Amakhosi's home form when speaking to IOL ahead of Chiefs' home league game against Free State Stars which will be played at the Moses Mabhida Stadium in Durban on Saturday.
“It is a worrying factor (that we haven’t won at home). Every team that comes to us wants to prove the point. They want to show their A game," Parker said.
"We need to wake up. It is our third season now without a trophy. It's not only our quality and our talent, it's all about our effort, attitude and our minds. If we can lift that a little bit, no team can stop us.
"It is only ourselves that is beating us because we allow other teams to step on our toes and overpower us. We let them win their battles in our home ground and when we go away for instance, the crowd lift us," he continued.
Amakhosi, who have kept two clean sheets on the road in the league, play their home games at the Moses Mabhida Stadium and FNB Stadium in Johannesburg.
“Our coach, the technical staff and players, we are well aware that our home record hasn't been what is expected in us. Our supporters in Durban always play a big role in our performances. We are back to our home away from home. Mabhida is our happy away home ground," he added.
"Hopefully things will work out for us. Last time we lost to Baroka. They wanted it more. We were a little on the back foot. They overpowered us with their energy. It was big learning curve for us.
"From there on we have stepped up a gear. Now we are back at Mabhida. We want to live up to expectations,” Parker explained.
Parker is wary of Stars, who have improved under coach Luc Eymael this season. Ea Lla Koto have recorded two wins, two draws and one defeat in their last five league games.
“Free State Stars are looking more lively, they are looking more positive. You can see their energy and the way they have been playing. We are aware that they haven’t played in quite some time so they will probably be fresher than us," he added.
"They will be more energetic. I think our game has gone more mentally now. We have to stay level-headed and try and play fast. We need maturity in our fast play. I believe that can change the results.
"The work ethic, commitment and heart is there. It is matter of using the mind more in our attacking play. We have to support and motivate one another and create more. We need creativity and always possess our A-game,” Parker concluded.
Chiefs are only three points behind log leaders Baroka.