Chiefs drew 1-1 with Orlando Pirates at FNB Stadium on Saturday afternoon.
Komphela was unimpressed with how the showpiece fixture was handled, saying immediately afterwards: "You know there are two things, it's elevation and relegation. We have got to elevate the Premiership. We cannot constantly relegate the product... that is very important.
"It's a big match. Maybe at some stage we shall be forced by circumstances to invite international officials. Officials can never be above the game.
"We are all participants and we expect the same in everything. Not thinking, not judgement, just a game to go home.
"I don't want to say this because behind me is millions of gold and yellow shirts. I wish I had an opportunity to speak on my own, unfortunately I represent.
"The game is very important, and all we are asking for, whatever the circumstances Pirates and Chiefs are big dogs. And every time they play, I don't know how to put it, they represent what South African football is about. And everyone involved does the same representation."
When asked about his utterances, Komphela said it was an opportune time to speak up.
"In Kaizer Chiefs, the ‘K’ has reference to something… The ‘H’ [in Chiefs], apart from hard work, resembles humility,” Komphela said.
"Had it been that we lost here [against Pirates], I would not even think of it lest it is interpreted as sour grapes. I’m better positioned now to say it, because even on the back of a result that was positive – a win – they would call it arrogance.
"So this is the best time availed to us to mention this because you have to put it in a way that won’t put you in a maze of: ‘Ja, because they won’ or ‘no, because they lost’.
"It is what it is but, the fact remains, what I said is not offensive but more suggestive. I think it is proper; there is nothing wrong with that because we’ve seen what happened today."
The former Free State Stars boss then revealed one of the assistant referees refused to shake his hand after the game.
"I strongly believe nobody should be above the game [of football]… At the end of the match, I tried extending a hand to the first assistant referee who was running just alongside our bench and he refused it.
"It reminds me of a colleague of mine, who at some stage tried to shake the referee’s hand – this is fair play, we make mistakes as it is an emotional game – and the referee refused to shake his hand.
"I felt bad because I though it is worth respecting when a man extends their hand. It is in the spirit of saying, ‘you know what, whatever happened has happened, we move on’ but if he holds grudges, unfortunately [shrugs]… not part of my profile, I move on in life."