Carol Aitken, who arrived at Edinburgh Airport with her children on July 14, said the company had provided a "complete lack of any support or information".
She said she had been unable to contact Menzies despite waiting hours at the airport and was shocked to find passengers' missing baggage forms left unattended at its desk in the terminal.
She told The Scotsman: “We waited almost two hours at [Edinburgh] airport for their arrival or for someone from Menzies who could help.
"There was no such person available, so we left without our bag, having filled in a report form and completed the online lost bag process.
"Since then there has been no word about our bag, despite repeated attempts to get some information.”
Menzies said Ms Aitken was later wrongly informed to go to its temporary baggage processing centre at the nearby Royal Highland Centre (RHC), where she was advised to go back to the airport because it was not yet open to passengers, to find the Menzies desk unstaffed.
She said: "Dismayed, but undeterred, I waited in the airport for two hours, all the while trying to get through to Menzies for some information.
"At the customer service desk, there was just a huge pile of customer lost luggage forms in a cardboard box.”
In an email to Menzies, she said: "Frankly, you should hang your heads in shame for this deplorable lack of customer care.”
A Menzies spokesperson said: “We acknowledge our customer service and, in particular, communication with passengers has recently fallen below the standards we expect and would like to apologise for the inconvenience this has caused.”
Its “baggage repatriation centre” at the RHC was now open for passengers to collect their luggage, or it would be returned by courier.
"We understand the distress and frustration being separated from luggage can cause passengers, and hope this new facility will enable passengers to be reunited with their bags as quickly as possible,” the spokesperson said.