Vanessa Hudson took over the top job earlier this month after former CEO Alan Joyce stood down following 15 years as one of the country's highest-paid executives.
In a video message released on Friday, Hudson apologised to customers for the airline's recent performance.
"I know that we have let you down in many ways and for that, I am sorry," she said.
"We haven't delivered the way we should have. And we've often been hard to deal with.
"We understand why you're frustrated and why some of you have lost trust in us."
The airline's leadership has been under pressure for weeks following a series of scandals.