The Ibrox club moved quickly to impose indefinite bans on the individuals involved and also barred their supporters club from receiving future tickets after videos were circulated online showing the Japanese forward being the target of racist songs and gestures.
Rangers had earlier condemned the footage, stating: "Those who indulge in such behaviour are not representative of our club or the loyal support who have stood by us through thick and thin.”
Celtic also branded the abuse “sickening and pathetic” and Parkhead boss Postecoglou insisted Rangers “did the right thing” with the prompt punishment against those who abused the 26-year-old striker.
Asked if he was impressed with Rangers' response, he said: "It doesn't matter who it involves, we don't need to be impressed. It just has to happen.
"I don't think Rangers acted because they wanted to impress anyone, I would like to think people see right and wrong and just deal with it.
"This doesn't need endless debates on radio or television on what should happen and why it happened. It is wrong, we know it is wrong.
"It is not something someone sees any grey in, I would be surprised because we all understand how people in that situation feel when you are the victim of something like this.
"They did the right thing in dealing with it and whoever else it happens to or whoever else wants to transgress, whatever organisation they are involved in, I expect it to be dealt with the same way.
"Just simple, deal with it and when the consequences come that quickly and without too much debate, I think people start to realise maybe a line has been drawn and we shouldn't really conduct ourselves in this way any more."
Postecoglou has insisted Furuhashi is “good to go” in the Europa League play-off second leg tie against AZ Alkmaar tomorrow, which the Hoops lead 2-0 from the first leg, and is still “really enjoying his time’” in Scotland so far.
The former Australia boss said: "Has he been affected? It's hard because unless you - it's the old adage - walk a mile in a person's shoes, how do you really know?
"He's a really positive character, he is really enjoying is time here, not just the football but living here in a new country and a new experience.
"And when 99 per cent of your experience is overwhelmingly positive, that one per cent, I hope anyway because I feel responsible and protective of him, doesn't affect his overall outlook.
"But it is easy for me to say, it hasn't been directed at me.
"But he is training well, he is a happy-natured guy and the club are supporting him, the players are certainly around him and he has been good.
"He understands this is not reflective of his experience here.”
Furuhashi, who has scored six goals in seven appearances since his £4.5m move from J-League side Vissel Kobe, issued his own message via social media message in response to the support he had received, echoing Celtic's 'You'll Never Walk Alone' mantra.
He wrote on Twitter: "I'll never walk alone #NoToRacism".