Clive Stokes, from Kidderminster, who travelled to Cyprus, said delays at the airport were “understandable” given the problems.
“But what the airport didn’t do is explain the situation to people.”
He said he had received an email on Friday evening, “two hours into our flight, saying there was a good chance our baggage wouldn’t be there”.
On arrival, only “about 20 cases” had came through, he added.
“I’ve probably spent between three and four hundred euros today on my credit card just to buy stuff, which, I think, I hope they’ll reimburse,” he added.
“It’s not the end of the earth, but there were people on the flight who were getting married, so they’ve got wedding dresses missing.”
Birmingham Airport said holiday company Jet2 had contacted all affected passengers, and other third parties were also working to reunite passengers with repatriated bags.
An airport spokesperson said: “We are continuing to experience an issue with our baggage systems which is impacting some outbound luggage.
“Engineers are on site and working to resolve this issue as quickly as possible. Terminal colleagues are also working hard to ensure baggage in terminal is being processed as quickly as possible.
“We expect this to cause inconvenience for some passengers, and we sincerely apologise for this. Those due to travel today, should still arrive at the airport in line with Airline advice.”
TUI has been approached for comment.
Some flights from Bristol Airport are being diverted through Birmingham after flights were suspended due to a runway defect.