Scots will vote in September 2014 about whether or not their country should remain part of the United Kingdom, with Labour former chancellor Alistair Darling running the "Better Together" campaign.
Margaret Curran told delegates Labour has much to do in the future if it stays and works together as a united party.
But she warned this could be threatened if the Scottish National Party (SNP) succeeds in its campaign for separation.
Ms Curran also claimed SNP leader Alex Salmond is putting the interests of his party ahead of those of the Scottish people.
The shadow secretary told the Labour Party conference: "If the SNP have their way, their plan will mean the break-up of the British Labour Party after 113 years.
"I want to send a clear message from this conference: That after 113 years, Alex Salmond is not going to bring our movement to an end."
Johann Lamont, Scottish Labour Party leader, told delegates: "We know opposition is frustrating and in these tough times unity and focus to secure power will never be at a greater premium.
"But how much more frustrating is it in Scotland when the Government behaves like a reckless opposition, refusing to take responsibility, happy to take any credit going and energetic in blaming others?
"And above all this truth - content to ensure that all those who could be protected are not helped.
"For that would be to show devolution working, devolution protecting. And if they allowed devolution to do what it was meant to do, how then they would achieve their own and only real ambition - for Scotland to be separate from the rest of the UK?"