Kiwi assassin Jeremy Brockie got the goal six minutes in after latching onto a floated pass from strike partner Bradley Grobler.
SuperSport were otherwise on the back foot, as Chiefs trio Hendrick Ekstein, Bernard Parker and Siphiwe Tshabalala all struck the woodwork at Durban's Moses Mabhida Stadium.
Komphela said: "As we are walking up here [to the press room], somebody said to me; 'nothing is wrong but something is not right'. And I'm saying, but wait a minute... that is confusing. 'Nothing is wrong but something is not right', so what you can say.
"Because we did everything right, did everything right; played football the way Chiefs are supposed to play the game and unfortunately we suffered a setback like Eric Tinkler has just put it. Around six, seventh minute; break attack we couldn't deal with, one zero and the rest is history.
"It is just that the ball did not get into the net. There was the Parker one where I said 'awu nkosiyami' [oh my God] this means the ball will not go in the back of the net.
"There's one Parker touched and where we are sitting you could see the ball going in and I'm saying it's going to hug the side-netting and it didn't. I'm sure by then Tinkler's heart was almost out, but congratulations to them.
"You can't fault the players, not at all. Because I thought they played good football. Forty-five thousand supporters, we appreciate their support. I think, apart from the defeat, they must have enjoyed themselves. Did we create chances, yes we did... I don't know."
When it was jokingly suggested to Komphela that he should consider performing a ritual to remove the bad luck, the former Maritzburg United boss took it in his stride.
"Has it gone to that level [of me performing a ritual]?" Komphela said in a response that got its fair share of laughs.
"The difference, in pressure and no pressure, is getting the round thing [ball] moving outside from hitting the upright inside and hitting the upright and going out. If then that is African, that Africanism taking it from hitting the upright out it should be upright inside, that is the only thing I can say.
"You can't explain this. Honestly. In as much as you respect the question because if you don't respond to the question, it is awkward. We take responsibility and you can't say no but you saw how the way we played... that is playing around games. You don't say that to people you respect."
Chiefs will open their 2017/18 Premiership campaign against Bloemfontein Celtic at Free State Stadium next Sunday.