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The Brazilians put four past Amakhosi with goals from Thamsanqa Sangweni, Tebogo Langerman, Lebohang Mokoena and Edward Manqele in a frenetic first half that stunned the Chiefs faithful.
Reneilwe Letsholonyane grabbed a late consolation for Chiefs while Josta Dladla missed a penalty.
Chiefs had hoped to at least match last season's run in the competition, wehre they lost 1-0 to Orlando Pirates in the final with Khune admitting his teammates felt humiliated by this outcome.
The Amakhosi captain told the club's official website: "The players are as humiliated as the fans by this result. I totally understand the frustration of the fans and would like to apologise to the fans that have been through thick and thin with this team.
"Things did not go our way against Sundowns but it is not the end of the world for us. We have a long season ahead of us. We are disappointed by the result but we know for sure that we can bounce back from this type of defeat.
"The opening stages of the game were a bit of a nightmare for us. We looked like we had switched off a little bit. We lost all the balls in the air. We let ourselves down but we have to bounce back as the team.
"We have a good technical team and a great squad of both experienced and young players. We know exactly what is expected from us. We need to redeem ourselves with a win against AmaZulu."
