Khune, who was beaten in stoppage-time by a Knox Mutizwa header at FNB Stadium on Saturday, reacted angrily to fans blaming him for the result, which ended Amakhosi's title hopes.
"The way I'm being attacked by people is like I always go on the field to cost the team yet I give 100 percent if not 200 percent in every match," was one of Khune's tweets on May 7.
The Bafana Bafana international has since issued a statement, which reads: "On Sunday 7 May, I sent a few tweets out of anger and frustration from my account. The action was triggered by messages received from some of my followers, some of whom were apportioning the blame of our 1-1 drawn match against Arrows towards me.
"The club has always emphasised that we need to be mindful when we use social media and should never tweet when emotional.
"I regret sending the tweets and would like to profusely apologise to all those followers who were offended. #Amakhosi4Life#LovePeace."