Thomas Cook customers struggled to apply for refunds after the claims website crashed shortly after opening.
Some users received error messages while attempting to input their details.
Aviation regulator the Civil Aviation Authority (CAA), which operates the dedicated website for Thomas Cook customers, apologised and said it had experienced “unprecedented demand”.
It urged people to “try back again later today”.
Twitter user @kevharrison_ posted a message to the CAA which read: “What the hell are you doing? You had weeks to make sure this system is robust.”
Another frustrated customer, with the user name @todd_alexandra, described the claims portal as “pointless and frustrating” before urging the regulator to “address this asap”.
The claims section of the website went live at 6am on Monday for those with future bookings for Atol-protected holidays to apply for a refund.
This relates to more than 360,000 bookings covering trips due to be taken by 800,000 people.
Atol-protected customers who were already abroad when Thomas Cook collapsed can also claim for the cost of replacing the parts of their holiday which were financially protected, or out-of-pocket expenses for delayed flights.
The CAA aims to pay refunds within 60 days of receiving a valid form.
The CAA’s final repatriation flight arrived at Manchester Airport from Orlando on Monday morning.
About 140,000 Thomas Cook passengers have been brought home from around the world on 150 aircraft during the past two weeks.
The vast majority of people flew on their original travel date.
CAA chief executive Richard Moriarty said: “The largest peacetime repatriation ever required an extraordinary effort from all involved.
“I want to thank everyone who has played their part in delivering this enormous undertaking, including the passengers we flew home for bearing with us as we undertook this complex operation.
“I also want to pay tribute to the many amazing former Thomas Cook employees who worked with us to make this operation a success.
“It needed an unprecedented team effort from our commercial partners, our friends across Government and my colleagues at the CAA.”
A union leader has stepped up criticism of the Government’s handling of the collapse of Thomas Cook by calling for ministers to be held to account for the loss of thousands of jobs and chaos for holidaymakers.
Manuel Cortes, general secretary of the Transport Salaried Staffs Association, will hold a meeting on Monday with Rachel Reeves, who chairs the Business Committee, to discuss the demise of the travel giant.
Cortes, who has called for the resignation of Business Secretary Andrea Leadsom over her handling of the crisis, said the Business Committee should question ministers and former Thomas Cook chief executive Peter Fankhauser.
Commenting ahead of the meeting in Parliament, Cortes said: “Everything points to negligence on the part of this Tory government and Andrea Leadsom in particular. She has admitted failing to hold a single meeting with Thomas Cook bosses in the days leading to the collapse.”
A Government spokesman said: “When a large company faces difficulties, it is standard procedure for one department to act as a single Government contact. In this instance it was the Department for Transport.”