The Chiefs captain says the defeat is a heavy blow, but insists the team can overcome the result with a win against AmaZulu in the League opener this weekend.
"The players are as humiliated as fans by this result. I would like to apologise to the fans that have been through thick and thin with this team," Khune tells Chiefs' official website.
"They once again came in numbers to support the team and we have to give something back to them starting against AmaZulu this coming weekend.
"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."
Khune says at the beginning of the match it seemed as if his team was not focussed, but adds that they have the depth to come back from the defeat.
"The opening stages of the game was 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 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.
"Great teams respond to defeat and we have to do it in the best possible way. Our objectives to turn things around as the team have not changed – it is a setback to be knocked out of MTN8 but the belief is still there that we can stand up and be counted come May 2013."