The Edinburgh-based company told The Scotsman that up to 3,000 bags have piled up at the airport due to baggage delays on connecting flights from hub airports such as Heathrow.
The firm said it was also understaffed, like much of the aviation industry, but was now “frantically training” new recruits.
Corporate affairs director John Geddes admitted the company had “dropped the ball” by failing to communicate properly with passengers, which he said was unacceptable.
Mr Geddes said Menzies had set up a special missing-baggage team over the past two weeks to work on the backlog.
However, he could not say when the problems would be resolved or how long the temporary storage facility at the nearby Royal Highland Center in England would be needed because airports such as Heathrow remain “under pressure”.
Mr Geddes said: “We are now in the center of the storm.
“The situation is relatively bad, so I would like to think that it will not get worse.”
The company apologized after the passengers arrived Edinburgh Airport without bags complained about the absence of Menzies staff and the inability to contact the company.
Mr Geddes said: “We apologize from the bottom of our hearts for the misunderstanding that has occurred, but we are under enormous pressure at the moment.
“If I were a consumer coming through the airport, I would completely understand the frustration and what we and the industry could do better.
“It’s simple things like making sure the desks are staffed, making sure the phones are answered, making sure the communications are top notch, and that’s what we’re working on right now.
“This is where we fell short of the standards we set for ourselves.
“It is unacceptable for the phone to go unanswered, and it is unacceptable for us not to communicate.
“We stopped communicating and I’m very upset about that.
“We apologize to every passenger who was not spoken to properly.
“People there will be more understanding if you communicate effectively with them.
“We are stressed, but things are getting better every week. We will make sure it doesn’t happen again.
“Our people at the airport are not people who don’t care – they don’t care.
“The bigger picture is that we want people to have confidence in air travel.”
Mr Geddes explained that most of the lost luggage was from passengers bound for Edinburgh and connecting at hub airports such as Heathrow, Amsterdam and Frankfurt.
He said, “If the hub is not working, all the spokes that come off the hub are really banging.”
Menzies, which operates 235 airports worldwide, handles baggage in Edinburgh for airlines such as British Airways and Lufthansa, with BA’s Heathrow-Edinburgh being the busiest in the Scottish capital.
He said “Edinburgh suffers from being a destination airport served by many airlines that fly through hub airports”, which he stressed has created a “mountain of bags”.
“There is a huge understaffing problem at Heathrow and some bags are not getting on the plane at all,” he said.
“We regularly have planes arrive in Edinburgh with 50 bags insufficient, or sometimes a plane arrives with 150 passengers but none of their bags.
“For planes to arrive without bags on board is unheard of.
“When planes show up with 150 bags missing, it throws your whole operation into chaos, especially if you don’t know it’s going to happen.”
Mr Geddes, who has been in the industry for 24 years, said: “I have never seen the scale of this.
“In the normal course of events you’d have one or two staff dealing with it, but this is off the charts – we had 3,000 bags at one point.”
He said the total was down to 600 by Tuesday, which would be processed “relatively quickly.”
However, he added: “The problem we will have is that there will be more lost bags on a regular basis.”
How long this will last “depends on how many missing bags arrive at Edinburgh Airport”.
Edinburgh-based luggage company Menzies Aviation has been hailed as a ‘disgrace to the nation’…
Mr Geddes said the staffing situation was improving at Menzies, one of three passenger baggage handling firms in Edinburgh.
He said: “We’re getting close to being fully staffed, but we’re short on skills and we’re training madly for the people we have.”
Sometimes the luggage counter staff had to be temporarily moved to check-in.
Mr Geddes said Menzies had called on the UK government to speed up security checks on new staff, which he said were taking “too long”.
He said the rules for issuing airport passes have been tightened since Brexit and now require evidence of applicants’ last five years of work – which can be seven to eight jobs.
Mr Geddes said: “We need to write to people, including in the hospitality sector, which is also under a lot of pressure and may not have the HR departments to handle the occasional inquiry.
“But if these people were working, HMRC records would exist and audits could be carried out through them.
“Sometimes the red tape of the UK government takes us 90 days to give people a pass into the airfield area.”
A UK Department for Transport spokesman said: “Last month we unveiled a 22-point plan to support the aviation industry, including fast-track national security checks to speed up recruitment.”
It said HMRC employment history letters with other guarantees could be used temporarily by the industry to carry out their checks.