The Accounts Commission said there was a risk services could not be maintained without improvements in the way the council was run.
But the report recognised that the council delivered good services at the moment.
The authority needs to save Â£22.3m - 10% of its budget - by 2017/18.
On top of that, council reserves are low and are projected to fall further, the report said.
The Accounts Commission is the public spending watchdog for local government in Scotland.
In its report, the commission said the council urgently needed "clearer priorities" in its transformation programme to ensure key projects were completed and savings made.
The report recognised the council's "commitment to improvement", but added that it was concerned about the pace of those improvements.
Deficiencies highlighted by the commission included financial control and management of resources.
The chairman of the commission, Douglas Sinclair, said: "There is a gap between the council's ambition and seeing evidence of that on the ground. This is what East Dunbartonshire needs to address if it is to continue to deliver good quality services in the future."
A public spending watchdog has published "serious concerns" over the financial control of East Dunbartonshire Council.