The Betway Premiership encounter at the Old Peter Mokaba Stadium ended with Amakhosi dropping two points, leaving them fourth on the league standings with 12 points from six matches.
Petersen's mistake allowed Polokwane City back into the contest and continued what has been a difficult start to the 2026/27 campaign for the 31-year-old goalkeeper.
The former Bidvest Wits shot-stopper has made seven appearances across all competitions this season, conceding seven goals and keeping just one clean sheet.
His current struggles are a stark contrast to last season, when Petersen played a key role in Chiefs' third-place finish and registered an impressive 18 clean sheets.
His form also saw him attract attention from the national team, with the goalkeeper included in the preliminary Bafana Bafana squad under former coach Hugo Broos ahead of the 2026 FIFA World Cup.
However, Da Cruz acknowledged that Petersen's display against Polokwane City was mixed, with the coach highlighting the saves he made before criticising the manner in which Chiefs conceded.
"Yes, for sure, it's disappointing (to concede like that) because, in the first half, Brandon Petersen made two great saves, but after that, I didn't see anything," said Da Cruz.
The French coach also pointed to Chiefs' awareness of Polokwane's threat from set pieces and crosses, making the manner of the equaliser particularly frustrating.
"We knew that Polokwane City are very good at set pieces and crosses. But when we concede this type of goal, it can be disappointing."
Chiefs will now look to put the result behind them when they return to Betway Premiership action against Golden Arrows on Sunday, 20 September.
The match has been moved to Mbombela Stadium, with Amakhosi aiming to return to winning ways and maintain their position near the top of the standings.
