Amakhosi opened the scoring through George Maluleka, but Kgoloko Thobejane's men replied with two goals to eventually claim all the points on offer and maintain their unbeaten record against the Soweto giants.
After the final whistle, Chiefs fans around the Moses Mabhida Stadium chanted 'Steve Must Go', and the coach needed police protection to leave the pitch.
The 50-year-old mentor said he understands the frustrations of the club fans, especially now that the Glamour Boys have been blowing hot and cold.
However, Komphela said there's nothing he can do about what the fans are saying about him, saying the growing calls for him to vacate his position don't necessarily mean the Amakhosi supporters hate him as an individual.
"It's about this job, you've got to take it. When they voice their opinion, you have to be frank and say, 'they are not happy with the result'," Komphela told SuperSport TV after the game.
"Do you think they hate you? well, something else but you, because they love their team and you deal with it," said Komphela.
"There's nothing you can do about what is said about you. The only thing you are in charge of is how you handle yourself. You still have to be dignified and stay focus, have respect and also have respect for them," he continued.
"You can't control anger from outside but you can control your emotions in terms of redirecting that anger and maybe showing some light," concluded Komphela.