The leader of Bristol City Council said the government funding settlement for the authority was "short-sighted".
Liberal Democrat Barbara Janke claimed cities like Bristol were being given "proportionally harder" reductions in their grants than other areas.
"Cities are the engines of the economy and contain areas of very high deprivation and need," she said
The council planned to save £22m next year but that figure will rise by £6m, the government announced.
"We have worked hard to prepare for the savings ahead," said Ms Janke.
"We were one of the first councils in the country to come forward with initial proposals and we still anticipate that our overall savings target of £70m over the next four years is correct.
"However, as we feared during the run-up to yesterday's settlement, the cuts have been frontloaded rather than spread evenly across the four years."
She added that the council would "ensure that frontline services were protected".