About half of the airline’s 300 aircraft are out of position. And in addition to pilots being in the wrong place, BA said there was severe disruption to rosters for its 4,000 cabin crew.
The airline is offering affected customers refunds or the option to re-book to another date of travel or an alternative airline.
Balpa said that the strikes had been a “powerful demonstration of the strength of feeling of BA pilots”.
Tens of thousands of flights had to be cancelled, costing BA an estimated £40m a day.
It called on the airline to come “back to the negotiating table with some meaningful proposals” to try to avert the next scheduled strike, on 27 September.
Balpa general secretary, Brian Strutton, said: “Surely any reasonable employer would listen to such a clear message, stop threatening and bullying, and start working towards finding a solution.”
Pilots had previously rejected an 11.5% pay increase over three years proposed by BA in July.
Balpa says its members have taken lower pay rises and made sacrifices during more stringent times for the airline in recent years.
But it says that now BA’s financial performance has improved – its parent company IAG reported a 9% rise in profits last year – they should see a greater share of the profits.
BA has said its pilots are already paid “world-class” salaries, and has described the pay offer as “fair and generous”.
After three years of the proposed pay deal, some captains could be taking home more than £200,000 per year, including allowances, it said.