Aiden Mccarthy broke the deadlock at the FNB Stadium after 38 minutes, but Mngqithi questioned the validity of the call, saying the goal should have been ruled out for offsides.
The result saw Arrows end the evening in 10th place on the league standings with 16 points from `15 games.
Amakhosi are in third place with 27 points from 15 games.
A number of coaches have questioned the standard of officiating in the South African top-flight this season, but far from blaming the referees themselves, the former Mamelodi Sundowns mentor explained that the whole system of officiating needs to be reformed.
The Video Assistant Referee system that is used widely across the globe is yet to be implemented by the Premier Soccer League.
"It's not what we were looking for, and it's worse when we lose from an offside goal," Mngqithi said on SuperSport.
"I do not want to blame the officials on this one.
"I think it's high time that the league looks at this differently because the reality is that the game has become too dynamic, and it's very difficult for officials to follow every movement.
"Even we see some of these things too late because we have a chance to look at the video footage, so we can't expect referees to be in touch with everything that happens in the game."
Arrows have now lost their last four league games and are next in action in the league away to Richards Bay on Saturday 30 January.