In a statement on its website this morning, BA says: "We understand the frustration and disruption BALPA's strike action has caused you".
He said it was a BA dispute and it would be resolved by the carrier rather than IAG.
A spokeswoman for the organisation, Lisa Kable, said travel insurance issues were not likely to apply as insurance only steps in when a "loss is incurred" and British Airways is offering full refunds or alternative travel arrangements.
The carrier, which is owned by London-listed International Airlines Group, said it has cancelled almost 100% of its 850 daily flights, affecting the travel plans of more than 100,000 passengers.
He said: "I'm really sorry for the position the cynical actions of the pilots' union has put us in". IAG, British Airways' parent company, made a net profit of US$3.2 billion previous year.
Pilots are unhappy with BA's offer of an 11.5% salary increase over three years.
"This strike will have cost the company considerably more than the investment needed to settle this dispute", according to BALPA.
Balpa's general secretary, Brian Strutton, said: "British Airways needs to wake up and realise its pilots are determined to be heard. Now BA is making billions of pounds of profit, its pilots have made a fair, reasonable and affordable claim for pay and benefits", he said.
Stuart Lloyd, Travel Expert at Columbus Direct commented: "Many of those heading off on holiday this week will experience severe disruption due to BA's pilot strikes".
All major USA airlines have profit sharing programs, but they vary in the degree to which they are successful in improving labor relations, said Adrian Yanoshik, a senior analyst at Berenberg.Done well, a BA program could be viewed positively by investors, he added.
The 48-hour walkout by pilots has resulted in at least 1,700 flights being canceled for Monday and Tuesday.
Passengers who think their flight will be impacted by the strike today or tomorrow can also access the "Manage My Booking" page to check their flight status. Pilots had to accept significant pay cuts during hard times, and now that the airline was making money, it should give something back to its pilots.
A further strike is penciled in for September 27. IAG's stock has fallen more than 31% this year, partly in expectation that the dispute with pilots would culminate in a strike, Berenberg's Yanoshik said.