Amakhosi were awarded a late penalty as Komphela's men thew everything at Pirates.
However, Willard Katsande failed to convert spot-kick as he shot straight at Brighton Mhlongo, who used his legs to make a save.
“I’m disappointed with what transpired and how things unfolded. This is a game of small margins and we didn’t come to the party. Pirates had more desire than us after regaining possession on the transition,” Komphela said post-match.
Komphela believes it is still way too early to rule Amakhosi out of the title race.
“There’s still a lot of football to be played and we just need to take it three points at a time. We can’t be obscured by the outcome,” Komphela added.
“If we scored the penalty, we would be talking a different story,” Komphela said.
Meanwhile, Pirates coach Kjell Jonevret echoed Komphela’s sentiments and rued the chances his side missed in the first 45 minutes.
“It was a fantastic occasion. Most countries around the world have nothing like this. South Africa should be proud of their Derby,” Jonevret said.
“We played really well in the first half. I wasn’t too upset when they scored because it was soft. (It was) their first attempt I think,” the Swede added.
“I think Chiefs were stronger in the second half. Got the ball quicker. Okay, we drew today, not great because we wanted to win. If I wanted to defend, I could have played other players instead of Ndoro,” Jonevret said.