Their career paths may never have crossed but the Celtic head coach is well aware of Smith’s standing in the Scottish game having led Rangers to 10 league titles, five Scottish Cups and six League Cups as well as the UEFA Cup final in 2008.
And Postecoglou insisted that the loss of the Ibrox legend will be felt in his homeland and across the world.
"Condolences to his family and all those close to him,” the Greek-born Australian said.
"I just heard the news and I can't recollect actually coming across him during my travels but I am well aware of his standing as a manager and his record at club and international level.
"More importantly you see the measure of the man with the people giving their tributes today. I just heard Ally McCoist who eloquently put it that he was just a great man.
"A sad loss for Scottish football, but he is someone like all of us who want to make our mark as people in our profession.
"I am well aware of his record at Rangers, with Scotland and with Everton. His standing in the game worldwide.
"Trust me I know him very, very well. The era I grew up he was one of those who you knew had a great standing in the game even from the other side of the world.
"I can assure you his loss will be felt globally and Australia absolutely. As I've said a few times there is a really strong expat community there."