The Australian defender won 12 trophies during his two spells at Ibrox, including five SPL titles and four Scottish Cups.
Moore went on to play for Newcastle United and Brisbane before rejoining the A-League club in his present role.
The 42-year-old said earlier this month he would leave Roar, but stay until March to help with players’ contracts.
But the Aussie club has now axed Sydney-born Moore after the fiasco of their midweek AFC Champions League clash with Philippines minnows Ceres-Negros.
Several players had to change the orange shirts midway through the 3-2 home defeat as the squad numbers peeled off their backs, with some using tape to improvise numbers as there were no replacement strips available.
Roar vice-chairman Chris Fong fumed: “We have a football director, and the buck stops with him.
“I was flabbergasted by the images I saw of the game. I couldn’t believe what I was seeing.
“It is disgusting that we could allow ourselves to be brought down to this level. It is indicative of what has gone on behind the scenes.”
Moore confirmed to a local newspaper that Fong has put him on leave for the remainder of his notice period.
Roar said in a statement: “The club understands the result against Ceres-Negros FC was disappointing, and the performance was unacceptable.
“We have always worn our orange jersey with pride. [On Tuesday] our club disappointed many people, and embarrassed ourselves with the presentation and numbering on our jersey.
“This was not the fault of BRFC kit manufacturer Umbro, and we are unreservedly apologetic.”
Moore was tipped to return to Rangers as a director of football last year.