An injury saw 'Shabba' miss the stalemate, which consigned fourth-placed Amakhosi to a second trophyless season under coach Steve Komphela with three games remaining.
Chiefs looked good for three points after Moon, an off-season signing from Maritzburg United, netted with a composed finish in the 77th minute at FNB Stadium.
However, fellow substitute Knox Mutizwa crushed the hosts' title hopes when he headed home in stoppage time.
Tshabalala told his official website: “The lads did well overall. We are just out of luck lately and it has not been going our way. That though is the way football is.”
The veteran, who recently amassed 300 starts for Chiefs, added: “The goal from the young man [Moon] was marvelous. I am happy he got on the score sheet and that will give him confidence to keep his head up and push on.”
The Glamour Boys next visit Polokwane City at Peter Mokaba Stadium this Saturday (18h00).