Spurs' appeal was dismissed following a Football Association hearing and the sanction stands, with the reasons for the decision published soon.
Bentancur has already been suspended for five domestic games, and will miss the English League Cup quarter-final match against Manchester United on Thursday as well as the visit of Liverpool in the Premier League on Sunday.
The club's Australian manager is already without a number of players due to injury and under pressure to stabilise an inconsistent season.
Appearing on a Uruguayan television show in June, Bentancur was asked for a Tottenham player's jersey and replied, "Sonny's?" He added it could be Son's cousin, too, because "more or less they are all the same."
Bentancur later apologised to Son on Instagram, saying it was a "very bad joke" and he would "never disrespect you or hurt you." Son accepted the apology.
Details of the decision released by the independent commission showed that Bentancur explained his comments "were sarcastic and a gentle rebuke" for the journalist calling his teammate "The Korean" and that he challenged the reporter's description of Son.
In its conclusions, the regulatory commission, however, wrote that "even on the basis of the player's evidence and submissions, we consider the player's conduct in using the words he did, in the full context in which they were used, was clearly abusive and insulting, and would amount to misconduct."
The commission added that it took into consideration the fact that Bentancur did not intend to offend Son or anyone else.
Bentancur was also issued with a fine of Stg 100,000 ($A200,000) by the commission.
