Tourism boss Norman Kinnish admitted the four-day airshow, which has left a £360,000 hole in the council's coffers, was a 'significant disappointment'.
He said it was 'important' that the financial breakdown was made public as soon as possible.
"There will be a review and we will welcome it," he added.
Mr Kinnish said some of the rising costs of the show were due to circumstances outside the council's control, such as the soaring cost of fuel bumping up fees for aircraft.
But he admitted that the income from ticket sales - £160,000 - was significantly below the £450,000 the council had budgeted for.
Programme sales were also far below the projected figure.
Mr Kinnish said £10,000 of additional income made during the four days was part of the seafront services budget, so did not show up in the Airbourne figures.
But he accepted the £191,000 predicted profit from the show had not been realised, and that the £360,000 variance against budget was a 'very significant sum'.
Councillor Steve Wallis, the council's tourism spokesman, said he 'shared the disappointment' of his cabinet colleagues and staff.
"I welcome the review," he added. "I have had many conversations with many people about Airbourne.
"There are lots of things we need to consider. People clearly do not want a raise in their council tax and people are reluctant to pay for Airbourne.
"It is a vital show for the town and we must do all we can to keep it in the town."
Council leader David Tutt said 'strenuous efforts' had been made to find ways to fund the annual show and 1,000 letters had been sent out to potential sponsors - without any luck.
"Clearly the charging did not work," he added.
The cabinet agreed to shore up the Airbourne cash crisis with money from the Strategic Change Fund.
But Councillor Graham Marsden, the council's shadow finance spokesman, said the Fund was intended for projects that will benefit residents.
"These figures make grim reading for residents, traders and hoteliers alike being far worse than the worst prediction.
"When commenting on the detail at the meeting the response of members of the Cabinet was disappointing in the extreme with expressions of regret at the loss but not a single apology nor acceptance of responsibility for this catastrophic business failure.
"What made it worse was the use of money from the Strategic Change Fund to pay off the debt and dig the Liberal Democrat administration out of a very deep hole of its own making.
"That money was intended to fund projects for the benefit of residents, support the local economy and plan the future of our town, not pay for costly mistakes by the administration. That means £360,000 of opportunities have been lost. What a mess."