A French disciplinary panel ruled that the 30-year-old was guilty of foul play and suspended him for 20 days until December 11.
But the Scots picked Hines for the visit of the Wallabies after an appeal against the ban was lodged.
The SRU had offered to send legal representation to the hearing but Perpignan told them it was a pre-hearing and neither the player nor a lawyer would be required to attend.
However, Hines was stood down late on the eve of the 44-15 defeat after talks between the SRU, the International Rugby Board and the Ligue Nationale de Rugby.
An SRU internal inquiry has now found gaps in knowledge about the complex disciplinary processes in other countries.
SRU chief executive Gordon McKie said: "Whilst I feel we made the right decision in standing down Nathan Hines from the Australia game, it came very late.
"I propose to strengthen our internal processes to ensure there is no repeat of this sort of situation in the future.
"Admittedly this was a particularly complex case but nevertheless there will be much better communication between the Scotland management team and administrative, legal and disciplinary advisers, moving forward.
"We must ensure a highly complex area such as discipline is fully understood, especially when it involves our overseas international players.
"There is no doubt these are complex areas where genuine errors can occur.
"However, our internal processes will be refined in the light of this episode and we will ensure that there is much greater consultation with the IRB over their interpretation of such regulations."
Hines said: "I was told by my club that there was to be a preliminary hearing to determine whether I needed to appear before a discipline panel, then learned I had been banned.
"That's where the confusion arose as I always denied the complaint and protested my innocence."