An elderly Tasmanian man who died from a head injury waited more than four hours at his home for an ambulance after being incorrectly triaged.

Alan Maurice Gray, 77, who had mobility issues, fell while pumping up his tyres at a Hobart service station on the afternoon of September 16, 2020.

He hit the back of his head and suffered bruising to his elbow and tailbone but was able to drive home after being helped by a member of the public.

He called an ambulance at 7.54pm on the basis of doctor's advice after developing a headache.

Paramedics arrived at 12.09am, finding Mr Gray, a retired botanist who lived alone, conscious and alert on the floor next to his reclining chair.

He was taken to the Royal Hobart Hospital where a scan revealed an extensive intracranial haemorrhage. Due to the extent of the bleeding, he was placed into palliative care and died two days later.

A coroner's report, published on Tuesday, found "an error" was made by the Ambulance Tasmania officer who triaged Mr Gray's call.

"(They) initially entered the case in the medical priority dispatch system as category '>6hr' meaning that the fall had occurred more than six hours previously," coroner Olivia McTaggart said.

"This was not the case and the correct entry should have been '<6hr', meaning that it had occurred less than six hours previously.

"This would have resulted in the case being allocated a higher response priority."

Ms McTaggart said she was unable to rule whether Mr Gray would have survived had he been taken to hospital earlier.

"However, the delay meant that he had no chance of recovery," she said.

Ambulance personnel called Mr Gray at 9.20pm and received no answer. The case was "not upgraded in priority as it should have been".

There were patient off-load delays at the Royal Hobart Hospital at the time, insufficient ambulance crews and a "generally high" caseload across Tasmania's south.

The facility has for years been plagued by bed block and ramping, in which patients can be kept in the back of ambulances because there is not enough hospital space.

Ambulance Tasmania has since improved education and follow-up measures relating to the dispatch system and introduced a call-back procedure for patients waiting for an ambulance.

"The department of health extends its sincere condolences to the family and loved ones of the man who sadly passed away," a spokesman said.

"The department is committed to continuous improvement and will carefully consider the coroner's report, noting no recommendations were made."