Cahill was sent off, before he had even come on, for abusing the referee after a controversial late winning goal from Melbourne Victory.
It was revealed that Cahill had called Chris Beath "a f**king disgrace" and urged Beath to "have a look at the big screen"
FFA handed Cahill a one match suspension, which means he will miss Saturday's match against Brisbane.
"I want to address what happened in the Derby on Saturday night. I sincerely apologise to Chris Beath for my reaction," Cahill wrote on Facebook.
"My behaviour also hurt the game so I also apologise to my team, to Melbourne Victory and to all the fans at the game and watching at home.
"Regardless of whatever happens on the pitch, I have to respect the game and the officials.
"I want the game to grow in Australia and I want to do all I can to help that happen. No matter the situation, I have to set an example and be accountable for my words and actions.
"My job now is to focus totally on football and winning as many games as possible."
