A 10-man Chiefs held on for the share of the spoils after defender Sibusiso Khumalo was red-carded for a reckless tackle on Thamsanqa Mkhize on the half-hour mark.
Amakhosi took the lead in the third minute through Michelle Katsvairo while Matthew Sim equalized for City FC in the 53rd minute.
"Up until we got red-carded it looked like we were on point, and even with the red card there were instances where you have to be opportunistic when you get those chances," Komphela told KickOff.
"The essence of playing with one man down is staying very disciplined and very strong mentally, which I thought, to an extent, we did but obviously as time goes the legs start giving [in] and you could see.
"Result; not that happy. Performance and commitment; you feel the players tried their best. We have to keep moving on without too many complaints."
Amakhosi fans were visibly upset after the game with some hurling objects at Komphela and his players, with the Glamour Boys going seven games without a win since their 2-0 victory over Ajax Cape Town on October 15.
Chiefs next face a tricky trip to the Nelson Mandela Bay Stadium where they will go up against Chippa United on Saturday.
Kick off is at 18:00.