The former Liverpool and Leeds United winger went over to talk to allegedly abusive supporters following his side's 4-0 defeat at Wycombe Wanderers on Saturday.
However, the incident is believed to have almost spiralled out of control, with Kewell reportedly having to be restrained by his own players and security.
"While I did approach a disgruntled fan at full time, it was merely to hear his concerns," the Australian said in a statement on the League Two club's website. "At no time did anyone need to hold me back.
"In hindsight, I should have just gone straight to the changing rooms given that emotions were running high. I apologise for any misunderstanding."
Crawley - who appointed Kewell in May - are 21st in League Two, with only four wins and 17 points from 18 league matches, and are without a victory in six league games.