Professor Alan Torrance of the University of St Andrews told The Scotsman he was “utterly shocked” at seeing distraught tourists trying to find their bags.
Thousands of bags are believed to have built up in and around the airport terminal which Menzies and fellow baggage firm Swissport are handling on behalf of airlines.
One Edinburgh Airport aviation source said: “It's a terrible situation. Things are awful.”
Prof Torrance had his luggage returned on Thursday, ten days after flying into Edinburgh with British Airways from Miami via Heathrow, despite the airline informing him his baggage had arrived at the airport on a later flight the same day.
The emeritus professor of the school of divinity said he and his wife had spent more than seven hours on the phone in fruitless attempts to track down their baggage, which contained valuable equipment.
He said: “As a university professor who served as an institutional auditor with the the UK Government’s Quality Assurance Agency for Higher Education, I am simply astonished at the baggage chaos being caused by Menzies Aviation at Edinburgh Airport.
“It is destroying the holidays of tourists to Scotland and is a disgrace to this country.
"Menzies Aviation is in complete chaos.
"BA confirmed my bag had arrived the same day on a later flight and that I should contact Menzies Aviation.
"They won't answer the phone, their office in Edinburgh airport is unstaffed and the booth at arrivals was unstaffed on arrival.”
The academic’s fears were increased because he said he was not issued with a property irregularity report (PIR) reference number at Edinburgh Airport for his missing baggage “and so was nervous about heading off without any documentation”.
Prof Torrance said he had then driven to Edinburgh Airport on Wednesday “in desperation and after nine days of anxiety”,
He said: “I was “utterly shocked by what I found.
"Queues of distraught tourists waiting in vain for hours at the unstaffed Menzies office.
"A Swiss couple were returning to Switzerland and hoping to pick up their baggage having not had them for their entire Scottish holiday.
"A Korean man had been coming every day hoping in vain to get his bags.
"When I found (a member of staff), he told me they didn't have the staff to repatriate the luggage, which was being shipped to a warehouse and simply continuing to build up.
"It could be weeks before anyone receives any luggage.
"I was left with no idea whether it would be weeks or months before the luggage turned up, or whether I would see it again.
“This is astonishing behaviour by a major company based in Scotland and a disgrace to the nation and our tourist industry, especially during the 150th Golf Open in St Andrews.”
Another passenger, former solicitor Dr Joy Barnard, from East Lothian, who flew into Edinburgh from Frankfurt with Lufthansa, told The Scotsman she had not been given a PIR number for her missing luggage by Menzies either, which she had requested 11 days ago.
Others were equally scathing about Menzies, with Richard Harrison writing on Google Reviews on Thursday: “Doesn't even deserve one star.
"There is nobody in baggage reclaim office, nobody answering phone calls and nobody on the front desk.
"All the staff seem to be hiding while the lost airline luggage piles up.”
Emma Hamilton wrote on Monday: “It has been seven days since I arrived at Edinburgh with no bags.
"I have heard nothing and no one is replying to any messages, picking up the phone or responding to emails.
"There is zero customer service, not just bad customer service.”
Menzies Aviation said it acknowledged the “distress and frustration” caused by mislaid baggage but insisted that claims it did not issue passengers with PIR numbers were “categorically untrue”.
Its spokesperson said: “Menzies Aviation is striving to uphold our high service standards for our airline customers and their passengers, despite the well-documented staff shortage and supply chain issues affecting the entire aviation industry.
Edinburgh Airport, amongst others, is currently experiencing the arrival of high volumes of unaccompanied baggage.
"This is not due to a single point of failure in the system.
"However, by default, unaccompanied baggage becomes the responsibility of ground handlers who are operating on behalf of airlines.
“We understand the distress and frustration this can cause passengers, and Menzies is working hard to minimise the impact of these baggage delays on passengers and to support the airlines with the current challenges.
"A dedicated team at a secure facility in Edinburgh is working hard to reunite passengers with unaccompanied baggage as soon as possible.
“Menzies Aviation complies with all necessary regulations and operating procedures, and claims that it does not issue PIR numbers to passengers are categorically untrue.”
Swissport, which handles baggage for airlines such as Jet2, Ryanair, Air France and KLM, said: “Unfortunately, a significant number of bags from a range of airports and operators are not being loaded onto connecting flights into Edinburgh.
“Instead, they are arriving on different, later flights after most passengers have already left the airport.
"The knock-on effect of these missed baggage connections has created a backlog of luggage to be processed.
“We understand this is a really frustrating situation for passengers and we're working closely with our airline and airport partners to process these bags as fast as we can.”