Flight compensation website Flightright.com said that with around 800 flights canceled at Gatwick and Heathrow on Saturday and Sunday, BA was looking at having to pay around 61 million euros ($68 million) in compensation under European Union rules.
"The worry for shareholders is that this unquantifiable impact could have longer-term consequences", he warned.
The IT outage had a knock-on effect on BA services around the world, while passengers who did get onto flights from the United Kingdom reported arriving without luggage.
IAG was down 4% lower as trading opened for the first time since the bank holiday weekend's widespread cancellations on BA's network.
The airline, which has traditionally positioned itself as an upmarket alternative to budget rivals like Ryanair, has come under fire in recent months for cutting costs in an attempt to compete with the growing number of budget airlines.
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Some passengers, however, were flown out of Murtala Mohammed International Airport in Lagos on Saturday by KLM Airlines, while others were flown to Heathrow-London by Virgin Atlantic on Sunday morning.It was gathered that the British Airways passengers who were not flown out on either of the flights were provided with complimentary hotel bookings.
"I'm working very closely with my team to make sure, again, that we work on the rest of the disrupted passengers to make sure that we address all of their needs".
The carrier blamed the IT fault on a power outage but one IT expert quoted by the BBC said such and event should not have caused "even a flicker of the lights". Ryanair, which reported record annual profits on Tuesday, had taken to social media to poke fun at BA. "That's our approach and we've never had a major outage".
"We have three IT locations in different countries across Europe, so if anything does happen, the second one kicks in and the third one will kick in", Chief Marketing Officer Kenny Jacobs told reporters as the group reported financial results.
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"We are very sorry for the frustration this situation is causing at a very busy time of year for holidays". This was typified earlier this year, when a decision to cut inflight meals on short haul flights was met with widespread criticism. "We are continuing to work to get delayed bags to customers as quickly as possible".
BA's Twitter account suggested a number of passengers should call 0844 493 0797 - which can cost up to 7p per minute plus access charge of up to 55p per minute.
David Hickson, of the Fair Telecoms Campaign, told the Sun: "BA is being greedy and foolish".
The airline said on Monday that everything was returning to normal.
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