The dramatic incident unfolded late in extra-time at Cape Town Stadium, with the score locked and a penalty shootout imminent.
Chiefs had prepared to bring on Bruce Bvuma, known for his penalty-saving ability, but Ntwari declined to leave the field despite being called to the touchline by Kaze and fellow assistant coach Khalil Ben Youssef.
Ntwari went on to save Stellenbosch's first penalty, yet it wasn't enough to prevent Amakhosi from suffering a 5-4 defeat in the shootout, crashing out of the competition.
Speaking after the match, Kaze played down the controversy, insisting that the goalkeeper's actions stemmed from a desire to help the team rather than defiance.
"I believe in that kind of situation, it's something that we're going to handle internally," Kaze told SuperSport TV.
"But he felt that he was comfortable to go on under the penalty and help the team. It was coming from a good intention. Maybe the way wasn't as good as it should be, but it's something that we will address internally."
The defeat comes at a turbulent time for Kaizer Chiefs, who recently parted ways with head coach Nasreddine Nabi. The loss has intensified pressure on the technical team, which includes Kaze and Ben Youssef — both of whom arrived alongside Nabi earlier this year.
Kaze remained diplomatic when questioned about his own future at the club, deferring to Chiefs' management.
"I believe that's a question that should be directed to the management," he said. "From this time, we are the coaches of Kaizer Chiefs, and until further notice or something else is decided by the management, I'm pretty sure they will let everyone know."
Chiefs will look to regroup quickly as they turn their attention to continental duty, with a tough CAF Confederation Cup clash against last season's runners-up Simba FC scheduled for October 17.