The former Rangers and Preston North End player is in a stable condition in hospital after what Albion say was an "accidental clash of heads".
Albion chairman Stuart Brown said the 27-year-old "clearly he faces a long journey to recovery".
Little joined the club in February.
After the incident on Tuesday, he was taken by ambulance to nearby Forth Valley Royal Hospital before being transferred to another hospital in Edinburgh.
Brown added: "I have been updated by the club medical staff that, whilst this was a serious and scary incident and Andy's injuries are substantial, he is now comfortable and stable in hospital and out of danger.
"I spoke to Andy's mum and she and his dad are making plans to travel to Scotland. I have assured her that SAFC will do everything necessary to assist Andy back to full health.
"I can't thank our club doctor, Andrew Deeley, our physio Kenny Crichton and the paramedics enough for their swift and expert attention.
"It is especially comforting that, within our club, we have personnel that have both the skills and dedication to handle such, hopefully rare, situations."
Little, who won the last of his nine caps for Northern Ireland in 2012, was released by Championship side Preston in June and has made five appearances for Albion.
He had spent time on loan to Blackpool and Accrington Stanley after failing to become a first-team regular following his move to Deepdale from Rangers.
Stirling Albion and Northern Ireland striker Andy Little has suffered a fractured skull and eye socket in a training-ground accident, the Scottish League Two club have confirmed.