The airline, part of the International Airlines Group (IAG), canceled 1,700 flights to and from London's Heathrow and Gatwick airports on Monday and Tuesday ahead of action by British Airline Pilots Association (BALPA) members in BA's first ever pilot strike.
"I am really sorry that the cynical actions of the pilots' union have put us in his position," BA Chief Executive Alex Cruz told BBC television.
"It is by all accounts an own goal; it's going to punish customers, it's going to punish our brand, it's going to punish the rest of the colleagues."
IAG shares were down more than 2% in early trading.
BA has offered its pilots an 11.5% pay rise over three years, which it said would take the pay of its highest earning captains from 167,000 pounds ($205,000), plus 16,000 pounds in allowances, to just over 200,000 pounds.
Its pilots on average earn around 90,000 pounds a year.
BALPA wants the pay deal to include profit sharing.
"British Airways is going through some good times, we want to share in those profits just as we shared the pain in the bad times," BALPA General Secretary Brian Strutton told BBC television.
He had said pilots were willing to compromise, but BA was not prepared to "budge."
The airline dismissed a new offer by BALPA last week as an "eleventh hour inflated proposal" that was not made in good faith. BALPA had said it would have called off the strikes this week if BA had engaged with the offer.
BA's Cruz said 11.5% was "way above" inflation and the offer already recognized that BA was making money. UK inflation stood at 2.1% in July.
Cruz said the airline was prepared to negotiate.
"The commitment of everyone at British Airways is to get over this particular dispute as quickly as possible and we urge the union to sit down with us as quickly as we can so we can reach an agreement," he told BBC radio.
He said it was a BA dispute and it would be resolved by the carrier rather than IAG.
The airline said it had no detail from BALPA on which pilots would strike, and had no way of predicting how many would come to work or which aircraft they are qualified to fly, so had no option but to cancel nearly 100% of its flights.
Following strikes on Monday and Tuesday, another day of industrial action is scheduled for Sept. 27.
BA has been criticized over its communications with passengers ahead of the strike, which has caused thousands of people to change their travel plans.
The UK Civil Aviation Authority (CAA) is investigating the airline after it enraged some travelers by wrongly telling them their flights had been canceled.
The regulator also reminded the airline to tell customers their rights. During the strikes, BA must offer passengers reimbursement for canceled flights, alternate travel arrangements under comparable conditions or a new flight at a later date.
A spokeswoman for Prime Minister Boris Johnson has urged both sides to end the dispute.