Nkhatha was booked twice in stoppage time - first for holding up play and then for showing dissent to referee Victor Gomes - after he replaced Dove Wome in the 69th minute at Bidvest Stadium.
The scores were locked at 1-1 at the time, with Wits previously having Buhle Mhkwanazi sent off in the 78th minute.
However, the Clever Boys then took control of the tie in extra time courtesy of goals from new signing Daine Klate and veteran forward Henrico Botes.
Matsatsantsa coach Gordon Igesund was clearly unimpressed with Nkhatha's "moment of madness".
“From that moment [when Jeremy Brockie scored in the 56th minute], we were totally in control of the game, and then a moment of madness,” said Igesund.
“If you get offered the opportunity where a player on the opposition gets sent off, you must take advantage of it. There was no way we were going to lose the game with 11 men.
“We had control of the game with 11 versus 11, and when they had a man sent off it was even better for us before the moment of madness, which I’m very, very annoyed about.
“I can’t say I’m disappointed [about the red card], because you know at this level you can’t do something like that… but I’ll deal with that internally.
“I don’t want to hang our washing out on the line, but I’m hugely disappointed about it and I’ll take care of that in the office,” he added.