The Warriors needed a win from their final Group B clash with Bafana but ultimately lost 3-2 with Oswin Appollis netting an 82nd minute spot-kick to kill off the tie.
Zimbabwe found themselves a goal down at Stade de Marrakech on Monday to a seventh minute Tshepang Moremi strike but were back on level terms after a super solo goal from Tawanda Maswanhise.
Lyle Foster put Bafana ahead again in the second half, but an Aubrey Modiba own-goal restored parity again to provide hope of an upset, until disaster struck.
Nakamba was adjudged to have handled the ball in the box after a VAR check, and Appollis sealed the win with his conversion.
Reflecting on the game, Nakamba told the Herald: "I am heartbroken. If there are people that I never want to let down, then it should be Zimbabweans.
"Even when I play club football, I play there to make Zimbabweans proud. And these are the same people that I have disappointed.
"I am really sorry. I don't know how to express this, but I am slowly sliding into depression with what I have just caused."