Ms Curran said she can understand why some people might think Yes offers the chance to “escape the Tories”, but said independence would mean even bigger cuts than the UK Government’s austerity programme.
She said her party must learn from past elections and fight for every vote in the referendum, insisting Labour “can’t afford to be complacent”.
Writing on the Labour List website, Ms Curran said: “If I thought an independent Scotland would improve the lives of people across our country, I’d be campaigning for it. But I know it won’t.
“The Labour Party can’t afford to be complacent. The SNP are trying to win over Labour voters, and we have to be out there fighting for every last one. We’ve seen in elections before what can happen if we’re complacent.”
She dismissed SNP calls for Labour voters to “vote Yes to reclaim the Labour Party”, insisting the nationalists have opposed Labour calls for an energy freeze, a 50p top tax rate and tax on bankers bonuses and “sided with the Tories”.
“During this campaign, I’ve been concentrating my efforts on Labour’s historic heartlands,” she said.
“And I’ve heard the same thing on doorsteps, in town hall meetings and on the street. People want change. They’re sick of the Tories. And they want more control over the decisions that affect their lives.
“I can understand why some people might think that voting Yes offers them the chance to escape the Tories.
“But with experts saying that Scotland would start its life with a bigger deficit than the UK, any future Scottish Government would have to make cuts that would surpass the Tories, or significantly raise taxes to make up the difference.”
She added: “Alex Salmond can carry on dismissing the real concerns that we’re raising from the people of Scotland, and promising jam tomorrow.
“We will be giving people hope for the future, a plan that we know we can deliver, and a reason to vote no with pride.”