Nick Forbes was responding after leader of the opposition Anita Lower referred to him having a three-quarters of a billion pound budget for public services.
The Labour leader has said in fact he has £548m to spend, which includes what he must spend on schools and housing benefit by law.
Anita Lower, Liberal Democrat councillor for the Castle ward, said she had made a mistake and knew full well what the council has to spend on services.
Councillor Forbes, who is planning to cut £40m from the city council’s budget in 2015/16, said the Liberal Democrat leader had shown she doesn’t understand the basics of the council finances.
He said: “This is even more shocking given that Coun. Lower, as well as being Leader of the Opposition, is in charge of scrutinising the council’s finances. They claim that the council gets £750m from the Government, excluding money for schools; it’s actually £548m including schools budgets of £154m.
“And virtually all of what the council spends is dictated by central Government through legislation.”
Councillor Lower said she admits to the mistake, but it was a slip of the tongue.
She said: “It’s a misunderstanding but if he thinks that’s not a lot of money, he should start explaining what he does with it.
“To the average person in the city that’s an awful lot of money, and it’s about explaining that money and how we use that and what residents are asking us for.
“I know what they’ve got and I hold my hands up to the mistake.”