Peter Box said that the £1.6bn Stronger Towns Fund, announced on Monday to help struggling communities after Brexit, would not make up for years of austerity and called it a "desperate" attempt to bribe MPs ahead of a vote on Theresa May's EU deal.
Just short of £200m will go to Yorkshire and the Humber, but less than half of that will be made available for local authorities to bid for. The rest will be dished out using a "needs-based" formula, the government said.
Wakefield Council indicated on Tuesday that they would explore the possibility of applying for some of the cash, but its leader was heavily critical of the amount available.
Speaking at a meeting of the council's Cabinet, Coun Box said: "The figure that's been allocated to the whole of Yorkshire is £198m. I think the figure for the Midlands works out at about £5 per person.
"I'm not sure what the figure is per person for Yorkshire is, but my guess is it will be less than that because of the size of the population.
"The amount that's been made available is derisory and in no way makes up for what's been taken from local government in recent years.
"It's clearly designed to try to persuade some MPs to support Theresa May's EU deal."
The government insisted that the cash would help "hardworking people reach their full potential" and said it would be used to create jobs, train workers and boost growth.
In a statement, Communities Secretary James Brokenshire said: "We have listened to people across Yorkshire and Humber who feel left behind by momentous changes to their local communities and I’m determined to provide the support they need to create a prosperous future beyond Brexit."
But Wakefield's Cabinet member for transport, Matthew Morley, said he was "appalled" by the announcement.
"What was the point of austerity?" he asked. "This doesn't make up for anything that's happened."
Coun Box added: "If you're desperate to try to persuade your own MPs to vote, then you'll do anything."