Bentancur has faced consequences for remarks he made during an interview that was broadcast on Uruguayan television in June.
The 27-year-old was also fined £100,000 by the Football Association as part of the punishment.
Spurs said in a statement that they "accept the guilty finding" against Bentancur, but "believe the subsequent sanction is severe".
When asked how big a blow Bentancur's absence would be, Postecoglou said during an exclusive interview with : "It's disappointing because he's been great for us this year.
Trending"He's one of the ones whose football has gone up a level. But we understood this was kind of coming and there was an acceptance from everyone that whatever the sort of penalties were… I fully support the club's decision to appeal the severity of the ban, but ultimately we know it's going to be for X number of games.
"We will work with Rodrigo through that and make sure within that time he has all our support in all the right ways so when he is available again he's ready to go.
"I haven't spoken to him since it came out. He's been away with Uruguay and he's not quite back yet. I'd spoken to him in the lead-up to it. As I said at the time, he understands he has made a mistake, he's prepared to accept whatever penalty comes his way and we as a club are going to support him.
"The one thing that's undeniable to me, because I know him, is he's an outstanding person. He's an unbelievable team-mate. He's a person of the upmost character that has made a mistake. I think when that happens our role is to support him in any way we can."
The former Juventus midfielder was asked to show the shirt of a Spurs player and replied: "Sonny's? It could be Sonny's cousin too as they all look the same."
While an apology from Bentancur was swiftly forthcoming, due to this being an "aggravated breach", an independent regulatory commission panel were required to either uphold the FA charge or dismiss the case.
Son said he and Bentancur remained "brothers" and "nothing had changed" after the Uruguayan immediately apologised to him, admitting he had "made a mistake".
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