Amakhosi produced a determined first-half display to come from behind and take a 1-1 draw into half-time of Saturday's Soweto derby, only to again go behind 26 seconds after the restart as half-time substitute Luvuyo Memela made an instant impact for Pirates.
Chiefs again succumbed to the forward midway through the second period at FNB Stadium as Memela completed a swift counter-attack to seal the victory, with the result seeing the Glamour Boys slip to fifth in the standings, eight points off the top with seven games remaining.
"I'm very disappointed in the result," Bafana Bafana international Khune told SuperSport TV after the game. "I think we were in control of the match in the first 15, 20 minutes and we made an error at the back which resulted [in the ball going into] the back of the net from [Thembinkosi] Lorch.
"Even in the second half, the first minute of the game in the second-half, another mistake that resulted [with the ball] at the back of the net.
"Pirates didn't beat us - they beat us on paper, but in reality, we gave them the goals. Those were freebies.
"We're feeling hard-done-by by our own mistakes. We have to go back and do our debrief and see what we did wrong."
Khune did, however, praise the efforts or Orlando Pirates's two-goal hero Memela, adding: "Congrats to Luvo, he came on in the second half, made the difference, he took his chances very well and that was the difference in the match."
He continued: "Well-taken goals [from Memela]. We were hit on the transition. Every time they [Pirates] got the ball, they made sure they are in the right scoring positions.
"We were caught napping, caught sleeping, we were caught switched off so we have to go back and see where we got it all wrong and work on it."