Ngaba Xulu opened the scoring for the Natal Rich Boys at the Richards Bay Stadium after just six minutes.
Lebohang Maboe restored parity from the penalty spot on 19 minutes but Xulu put Ronnie Gabriel's team back in the lead with 39 minutes on the clock.
Siphesihle Ndlovu then found a 77th minute leveller for a share of the spoils.
For Amakhosi this was their second draw of the new season after holding Mamelodi Sundowns to a 1-1 stalemate, but their first points against Richards Bay - after three previous successive defeats.
The result left the Soweto club in third place on the league standings with eight points from four games.
Speaking after the game, a disappointed Da Cruz told SuperSport: "We lost two points today.
"We played a very good game, we were better than the opponents.
"We drew not because the opponent was better but because we made too many mistakes."
One positive for Da Cruz was the introduction of Asanele Velebayi, who set up Ndlovu for the equaliser shortly after his introduction.
"Since the beginning our substitutes have made good jobs when coming on," added the head coach.
"We need to keep this mindset because we don't only need 11 players but the whole squad."
Chiefs are next in action at home to Siwelele on 5 September.
