Mr Murphy said Ms Sturgeon had made a “stupid strategic error” by setting out a timetable for a vote on devolving full control over tax and spending to Scotland, when she took part in a BBC Scotland televised debate with other party leaders.
Under the SNP’s plan for full fiscal autonomy, Scotland would be responsible for raising enough cash to cover all of the country’s public spending.
However, Labour claimed that research by the Institute for Fiscal Studies showed this would leave a £7.6 billion blackhole in the nation’s finances.
Mr Murphy challenged the SNP leader on the issue in two back-to-back TV leaders’ debates, which he said had left Labour with a “spring in our step”.
The Labour leader who was campaigning in Cumbernauld, North Lanarkshire, said: “What we saw last night in the debate was Scotland’s First Minister admitting under her plans Scotland would be £7.6 billion worse off - it’s full fiscal austerity.
“We will oppose Tory austerity by the front door and we will also oppose the SNP’s austerity by the back door. We will keep the Barnett formula today, tomorrow, forever.”
Mr Murphy added: “There’s no way on earth we will vote for full fiscal austerity, or full fiscal autonomy.
“It’s more than £7 billion of cuts for Scotland. Why would anybody who loves our country want to cut that £7 billion?”
He also argued that changing the way services in Scotland are funded would mean the end of the UK pensions and benefits system north of the border.
“If the SNP have their way, you would have the abolition of the UK state pension here in Scotland and the abolition of UK benefits,” he claimed.