Chiefs' hopes of winning silverware in their third season under coach Steve Komphela ended with a 1-0 loss at Bidvest Wits in the semi-finals on Saturday.
The Glamour Boys next visit AmaZulu in the Premiership on Wednesday looking to reel in log leaders Baroka, who are two points ahead with a third of the season gone.
Komphela's men recently thumped mid-table Usuthu 3-0 in Durban in the TKO.
"We, as players, clearly understand what we want to achieve during this whole campaign," Parker told his club's website.
"We know that it’s about togetherness – as players, with the office staff and, above all, with our supporters. We are one family, forming a strong unit. Together we will become better and will achieve."
Parker was speaking as part of a promotional push for a new 'únity' t-shirt released by the Soweto giants.
"That only reiterates the cause to be ‘one team, one family’. It’s about encouraging and motivating each other. To clap each other’s back and to support as well as show love for each other. That’s what the words on the t-shirt represent."