Qatar Airways has halved the losses it predicted for the last financial year, Mr Al Baker said at the event.
Qatar Airways posted the apology to its Twitter account on Wednesday.
The airline was also the first to employ female pilots and one of the first to train female engineers, al Baker said, adding that several ranking positions within the company, including Senior Vice President, are held by women.
When asked what the association - long regarded as one of the world's most powerful "boys' club" - meant to do to increase the representation of women in the senior ranks of Middle East aviation, he responded: "That's not the case at Qatar Airways". There were loud groans of disapproval from many reporters in the room.
He insisted there was no gender inequality at the Gulf carrier, which enjoys a close business partnership with British Airways, as well as being the largest single shareholder in BA's parent company, IAG.
Qantas chief Alan Joyce said at the same press conference that the Australian carrier had achieved a strong turnaround in profits partly due to its pursuit of diversity, with women making up 40 percent of senior management. "If we're leaving out nearly 50 percent of the population in our search for the next generation of 640,000 pilots, we're clearly not tapping into all of the talent that's available", Alan Joyce, the airline's chief executive, said in a statement a year ago.
"I was only referring to one individual".
Al Baker's apology was shared by Qatar Airlines.
"It will be my pleasure to have a female CEO candidate I could then develop to become CEO after me", he continued.
"The comments made today are not shared by myself, or Heathrow airport".
Cathay CEO Rupert Hogg said there were no immediate vacancies on the top team but there were women managers a level below and diversity was valued at the airline, which has staff from 75 nationalities and is a supporter of the Gay Games 2022 in Hong Kong.
"If we're leaving out nearly 50 per cent of the population in our search for the next generation of 640,000 pilots, we're clearly not tapping into all of the talent that's available", Alan Joyce, the airline's chief executive, said in a statement this year.