Labour and Tory councillors who are part of the ruling coalition between the parties said they were standing up for "symbols the men and women of Stirling have fought and died under for 300 years".
However, Tory Callum Campbell and Labour's Danny Gibson cancelled their motion hours before a meeting at which it was expected to be passed.
Cllr Gibson blamed the decision on "an atmosphere of negativity". Cllr Campbell said it had been undermined by "the vitriolic tone of Nationalists".
Dr Peter Lynch, a history and politics lecturer at Stirling University, said the episode had made the city and council look dreadful.
He said "It's like Alex Salmond and the Saltire at Wimbledon. It probably seemed like a great idea, but it badly backfired. If Better Together are promoting this dual identity thing replacing flags has hardly been the way to do it. The Yes campaign have probably been cheering all day at this and people will ask 'did they withdraw this motion off their own back?'."
The proposed motion read: "Council resolves to stand up for the symbols of our country by flying the Union flag from the main pole above the council building and the council flag from the freestanding flagpost in the ground of Old Viewforth."
The councillors had claimed the promotion of the Union flag as the main symbol above Stirling's headquarters, alongside a Saltire, would also bring it into line with the Scottish Parliament.
Cllr Gibson, who seconded the motion, said: "We wanted a serious and mature debate about the future of our country, but this is not possible as an atmosphere of negativity has developed. There is much to discuss with regards to Scotland's place in the UK, the future of our country and the effect this will have on Stirling."
Cllr Campbell, who proposed the motion, said: "This debate has become distracted and undermined by the usual vitriolic tone of debate that Nationalists adopt.
"Instead of focusing on the successes of the social, economic and political union that are a bond that nationalists want to cast aside, they decided to focus on a minor part of the motion that gets their supporters worked up.
"I don't want this motion to become a distraction from the real issues of uncertainty that the SNP are asking us to decide upon next year, so I have written to the Provost withdrawing my motion."
The SNP's Graham Houston said: "The people of Stirling will decide on independence on the strength of the arguments and not foolish notions like this. The council can now focus on delivering services, which have been undermined by this administration."