Komphela resigned from Chiefs in April after a Nedbank Cup semi-final loss to Free State Stars condemned the Soweto giants to three years without silverware under his watch and triggered a fan riot at Moses Mabhida Stadium.
Ex-Free State Stars mentor Giovanni Solinas has since taken over the reins at Naturena.
Asked for his opinion on why the Glamour Boys failed to deliver under Komphela, Khune said: "We’ve tasted victory, having won trophies under coach Stuart Baxter. He left and we were struggling a bit under coach Steve, because a lot of us couldn’t adjust to what he wanted from us as players. But with the new coach, Solinas, hopefully things will turn around."
Komphela, who was recently appointed as Bloemfontein Celtic's coach, had little to say in response.
"Three years at Chiefs, I had the best of my time. I remained highly respectful and dignified. I'm not going to spoil that," Komphela said at a gala dinner for the Under-21 SAB League National Championships in Greyville, Durban.
Asked if he had any advice for Solinas, Komphela adopted a similar tone.
"No, no, no, I've always refused. Even in my past three years I've always refused. That's why for three years you had been hunting, hunting and hunting me, and I've survived the years of onslaught.
"I can not therefore commit an error today after having committed three years of no errors. I cannot then get excited and commit an error today ... it'll erase the three years of dignity and respect.
"Out of the sincere suffering I went through, I don't want ... I cannot. I'm going to still stay the same way I have been for the past three years; dignified and respecting irrespective [of the] circumstances."