"We understand the frustration and disruption of BALPA's strike action has caused you". "After many months of trying to resolve the pay dispute, we are extremely sorry that it has come to this", said the airline.
British Airways said it was "ready and willing" to resume talks.
"It is by all accounts an own goal", the airline's chief executive, Alex Cruz, told the BBC.
The association also pointed to a almost 10-percent jump in pre-tax profits reported by BA's parent firm, IAG, last year.
British Airways only operates one flight itself to Australia, from London to Sydney via Singapore and Monday's flight arrived just after 5am, flight boards showed.
BA says that passengers can request a full refund, rebook the flight for another time in the next 355 days, or use the value of your fare to fly to a different destination.
BA said other labor unions, representing almost 90% of all BA staff, including engineers, cabin crew and ground staff, had accepted the 11.5% increase.
British Airways logos are seen on tail fins at Heathrow Airport in London, February 23, 2018.
The strikes were voted for by 93 per cent of BALPA BA members.
The airline has estimated that the two-day strike that started on Monday will affect 195,000 customers. Now BA is making billions of pounds of profit, its pilots have made a fair, reasonable and affordable claim for pay and benefits.
Pilots vowed to strike following a breakdown in talks over a new contract. BALPA had said it would have called off the strikes this week if BA had engaged with the offer.
Balpa General Secretary Brian Strutton said he didn't recognize the figures and that most of the union's members at BA will earn a lot less.
Pilots had to accept significant pay cuts during hard times.
Passengers should find out via email whether their flight is definitely cancelled.
And it has been harder hit by industrial action than Ryanair, which reported no travel disruption after its British-based pilots went on strike this month.
BALPA is scheduled to hold another strike on September 27.
BA has been criticized over its communications with passengers ahead of the strike and the U.K. Civil Aviation Authority (CAA) is investigating after it wrongly told some travellers their flights had been cancelled. Passengers that are affected have been rebooked with other airlines or given alternate dates to fly, the BA spokeswoman said. 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.