Postecoglou says he accepts the FA's guilty verdict and that Bentancur will miss a number of matches.
In the media interview in question, asked by a presenter for a Tottenham shirt, Bentancur replied: "Sonny's? It could be Sonny's cousin too as they all look the same."
He later apologised on social media and said his comments were a "very bad joke".
Bentancur also said sorry to South Korea forward Son, who said his team-mate would "not mean to ever intentionally say something offensive".
Bentancur, who denied the charge, was fined £100,000 and ordered to undergo a face-to-face education programme.
The ban means Bentancur will miss Premier League matches against Manchester City, Liverpool and Chelsea among others, as well as a Carabao Cup quarter-final match against Manchester United.
He is available for Europa League matches.