He singled out club captain Zitha Kwinika and his assistant Innacio Miguel.
Chiefs were eliminated 5-4 in the shootout, with both Kwinika and Miguel notably not stepping up to take penalties.
This left Tashreeq Matthews with the crucial fifth kick - a chance to seal the game - only for him to miss, while Dillan Sollomons' sudden-death penalty was also saved, handing victory to the Cape side.
"You must have a team with a leader who leads by example, and I don't see that happening," Maponyane said during an interview on Radio 2000.
"If you look at Miguel, you think the guy is not really in charge. Then you look to see who can take charge, but I don't see anyone because they have not shown leadership at all. You need that leadership on the pitch. You don't always need it on the bench."
The former striker also questioned Chiefs' decision-making and composure during matches, highlighting players' erratic play and rushed decisions. He cited winger Glody Lilepo's excessive pace as an example of uncoordinated play.
"Sometimes you have to make changes as a captain and explain them to the coach later. You don't wait for the coach to say, 'Can't you see we are suffering here and there?' That leadership is not there, and I just wonder what goes through their minds when they play the same way all the time and rush things," Maponyane added.
"I don't understand when Glody Lilepo goes 200 km per hour and goes off the pitch. I ask myself if the ground is too small or if the guy is too fast. All those things are confusing sometimes."
Maponyane's critique highlights deeper issues in Chiefs' leadership structure, raising questions about on-field authority and decision-making as the club seeks to rebound in the remainder of the season.
Kaizer Chiefs were unable to find a way past Golden Arrows as the sides played out a goalless draw at Mbombela Stadium on Sunday, with both teams spurning opportunities to claim all three points.
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Kaizer Chiefs midfielder Siphesihle Ndlovu has expressed confidence in the ability of the replacements for injured duo Brandon Petersen and Wandile Duba.
Kaizer Chiefs will be looking for all three points from their Betway Premiership clash with Golden Arrows at the Mbombela Stadium on Sunday and the chance to avenge their recent MTN8 exit.
