The 33-year-old was recorded on a stump microphone telling Anderson to expect a broken arm in the latter stages of the first Test in Brisbane shortly after the England bowler, who was batting at the time, had confronted George Bailey.
"It's unacceptable that the Australian cricket captain is setting that example," Clarke told reporters. "But I don't regret standing up for George Bailey one bit.
"I just regret that everybody heard it and the language I used.
"The last thing I want is for boys and girls watching cricket to be going and playing club cricket and saying things like that to opposition players."
Clarke was fined 20% of his match fee by the International Cricket Council for the incident.