British Airways has been urged to automatically compensate passengers caught up in the bank holiday disruption rather than wait for them to submit claims.
Consumer group Which? claimed the airline is in "grave danger" of failing its customers again unless it goes beyond the legal requirements in response to flight cancellations and delays.
Some 75,000 passengers were stranded after an IT shutdown following a power surge on May 27 caused travel chaos for three days.
Under EU law passengers can claim compensation from BA for travel disruption, worth up to 600 euro (£524).
They can also claim expenses for items such as hotels, meals and phone calls.
Which? believes the carrier should automatically issue statutory compensation to all affected passengers, to "reduce the burden on passengers" and enable the airline to focus on dealing with the individual additional items.
In a letter to BA's chief executive Alex Cruz, Which? managing director of home product and services Alex Neill wrote: "Opting to do the bare minimum when compensating your customers for your failure to deliver the service you promised will undoubtedly cause further stress, inconvenience and financial hardship for passengers, and of course further damage to BA's reputation.
"As you will know, the rules around compensation in this sector are out of step with other markets, like energy and water, where compensation is automatically awarded to customers for severe disruption to, or complete absence of, service.
"Given the scale of the problem BA has experienced we strongly believe it is only right that you do more than the legal minimum.
"By simplifying the compensation process, you have an opportunity to minimise the additional stress and inconvenience you cause your customers and ensure they are not pushed into the arms of claims management companies, who will take a large part of the money they are owed.
"British Airways can, and should, seek to automatically issue statutory compensation to all affected passengers."
The letter follows a claim by the Association of British Insurers that passengers seeking compensation are being ''passed from pillar to post'' because a form entitled ''Make a claim for disruption expenses'' on BA's website orders customers with travel insurance to claim through their insurer in the first instance.
A BA spokeswoman said: "We sincerely apologise for the difficulties and frustration customers faced during the huge disruption across the bank holiday weekend.
"We will fully honour our EU compensation obligations and have set up a link on the home page of our website to enable customers to submit their claims as quickly and conveniently as possible.
"We have no desire to be obstructive in any way and have put additional resources into our call centres to process claims as speedily as possible."