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."

It happened at about 12:30 BST. The victim died at the scene.
Another man is in a critical condition.
The road is expected to remain closed for a number of hours while a thorough investigation into the crash is carried out.

Andrew Apperley, 38, from Eastbourne, was reported missing after failing to return to his hotel four days after going to a Full Moon party.
Richard Apperley said the situation was "just heartbreaking".
"My mum lost her husband and now she's lost her youngest son... it's created a big loss in our lives," he said.
"He leaves a young daughter as well."
Mr Apperley, who was raised in Gloucestershire, flew to Bangkok before travelling onto the resort island of Koh Samui.
On 12 February he headed by boat for a party on the island of Koh Phangan.
His brothers found a series of text messages sent to friends on 13 February appearing to suggest he may be in danger, including one mentioning  a "scary guy with the face mask".
His body was found four days after he was reported missing on 17 February.
Richard Apperley said he owed it to his brother to press the Thai authorities to investigate, adding he suspected foul play.
"I can't sleep at night, I've been up for days and days sat at the computer running a social media campaign which has gone global.
"I'm not go to go away and they need to deal with this."
He added the family plan to fly out to Thailand in the next few days.

Players did not speak to the media before and after Friday's 2-0 friendly win over Romania in Falkirk.
Their stance comes as Anna Signeul's squad prepare for next month's Euro 2017 finals in the Netherlands.
The Scottish FA said in a statement that it was "disappointed they have chosen not to undertake their media responsibilities".
But the governing body hopes to resolve the matter before Tuesday's friendly against Sweden in Vaxjo.
"We can confirm that we are in discussions with the Scotland Women's national team players regarding terms and conditions ahead of the women's Euros in the Netherlands next month," it said.
"We will endeavour to resolve this matter at the earliest opportunity through discussions with their advisors."
Scotland's home-based players are being funded to go full-time as they prepare for the finals, where Scotland meet England, Portugal and Spain.
A package agreed between the Scottish Football Partnership, Sport Scotland and energy firm SSE will provide finances until the tournament is over.
Around half the squad are expected to benefit from the scheme.
Head coach Signeul distanced herself from the dispute, saying she feels coaches should not be involved as it is between the players and the SFA.
"I'm not involved at all in that process," said Signeul, who suggested it was the same for men's head coach Gordon Strachan.
"They do this on the men's side as well, they negotiate contracts.
"It is between the SFA and the players and I don't think Gordon has anything to do with this either, it's nothing to do with us coaches."
Signeul will name her squad for Euro 2017 on 20 June.
A public spending watchdog has published "serious concerns" over the financial control of East Dunbartonshire Council.
[NEXT_CONCEPT]
A man has died following a two-vehicle collision on the A1 carriageway at Banbridge on Tuesday.
[NEXT_CONCEPT]
The brother of a British tourist found dead after a beach party in Thailand says he suspects foul play and want answers from the authorities.
[NEXT_CONCEPT]
Scotland's women are refusing to carry out any media or commercial activity due to a dispute with the Scottish FA.