The announcement of his resignation came just over 12 hours after Arrows had twice come from behind to pull off an upset 3-2 win away against Wits in the first round of the Telkom Knockout.
A club statement quoted the 42-year-old Mngqithi as saying: "When results are not forthcoming it becomes a situation which one needs to be realistic about it, and make decisions which are for the good of the entire club.
"Sometimes a change can have a positive effect and change the fortunes of a club. This is a club which has great potential and I believe it is only a question of time before things improve"
The win over Wits was only the second of the season for Arrows. Their other success came in the league at new boys Polokwane City on September 15. They have lost four of their six league games and, with just four points, sit just above the relegation zone.
But on Friday night, Mngqithi suggested his side were finally beginning to find form in front of goal, only to drop a bombshell the next day.