Mr Jones said he, Mr Brown and a senior adviser, Theresa Stratton, attended from the mayoral office.
Last night, a council spokeswoman said the council finance team hosted a function for around 50 staff from 4pm to 6pm at the Herald Theatre.
"The cost for food and beverages was $1297.60 excluding GST. The event was held to recognise the significant contribution of staff over the past 18 months on the development of the 10-year budget. The event was attended by staff, the mayor and a number of councillors."
Councillor Penny Webster said she attended the function between 5.15pm and 6pm.
"It was hardly a party, it was a few drinks for the staff. Doesn't the Herald have a few drinks for its people when they work bloody hard?"
She said the drinks and nibbles were put on by the finance team and "one or two" other councillors, who she would not name, went as well.
Manukau councillor Arthur Anae said he didn't attend the event and saw how it could look bad, being at the expense of ratepayers. "But council staff were working hard for 18 months, sometimes around the clock, to get that budget done."
But Albert-Eden-Roskill councillor Christine Fletcher, who did not attend, called the party "inappropriate".
"I think we have nothing to celebrate, I think we do not understand the pain that we are about to inflict on a lot of Aucklanders."
She said the council needed to count the cost of every dollar it spent.
Ms Fletcher said she was unhappy about the budget and had felt disheartened since it was passed.
"I think this is a real low point for Auckland and its amalgamation."
North Shore councillor George Wood said the budget wasn't something he felt like celebrating after Thursday's council meeting.
"I don't know how many councillors went ... It wasn't something that I was wanting to go to."
Orakei councillor Cameron Brewer also didn't attend and said: "The finance staff have worked really hard over many months. But the reality is in the public sector you've got to tread that much more carefully, particularly when the paying public is about to be stung a lot more."
Councillors Mike Lee, Callum Penrose and Linda Cooper said they did not go and Albany councillor Wayne Walker provided no comment.
The remaining 11 councillors did not return calls last night.
The budget will set an average 9.9 per cent rise in residential rates costed at $214 for the average household. Residents of the Mangere-Otahuhu Local Board area - part of Mr Brown's heartland of South Auckland - face the highest average increase of 16.9 per cent.
About 34,000 Auckland household will pay more than $500 when they open their latest bills in six weeks, and of those 9000 households will pay more than $1000.
As well as large numbers of Aucklanders facing hefty rises, the council said about 22.5 per cent of Aucklanders, or 102,000 households, will get a rates decrease.
Waiheke and Great Barrier Island and Rodney have average rates decreases of 2.8 per cent, 13 per cent and 1.4 per cent respectively.
Mr Brown has conceded a "significant" number of ratepayers will face a rates rise much bigger than the 2.5 per cent promised earlier by the mayor.
"What we passed yesterday was an increase, this year at least, and over the next 10 years, of an average of 2.5 to 3.5 per cent increases in the underlying rate take.
"We also passed a transport targeted rate of $114 net for every household," he told Radio New Zealand.
"And so for some households on top of what they're getting for their revaluation, yes, they will get significant increase in their rating," Mr Brown said.
The council is encouraging anyone facing difficulties paying rates to contact it for details about a number of options.
They include weekly, fortnightly or monthly payments; a Government rebate up to $610; and a rates postponement scheme.
The ratepayer-funded party preceded the appointment by Mr Brown yesterday of former Waitakere Mayor Sir Bob Harvey to a new role, Champion for Auckland-Overseas Investment.
Sir Bob stepped down this month from chairing Waterfront Auckland for five years to facilitate international investment opportunities and lead the council's $130,000 bid for the Lee Kuan Yew World Cities Prize.
He bolsters the council's push for overseas investment, which includes staff in London, San Francisco and Melbourne.