Both party leader Ed Miliband and shadow chancellor Ed Balls have said their would be cuts when Mr Murphy's claims were put to them, and shadow business secretary Chuka Umunna said on the BBC Daily Politics: "The leader of the Scottish Labour Party will not be in charge of the UK budget."
Ms Sturgeon said:
"The truth is out about Labour spending cuts. Jim Murphy's false claims in the TV debates have been rubbished by his own party bosses at Westminster, who have hung him out to dry.
"Labour would impose swingeing spending cuts on Scotland and the rest of the UK, carrying on with austerity where the Tories left off - that is the core aspect of the manifesto they have published. It sweeps away Jim Murphy's pretence, and leaves him devoid of any credibility in this campaign.
"Ed Miliband, Ed Balls and Chuka Umunna have just confirmed that Labour in Scotland continue to be no more than a branch office of Westminster Labour. That is why so many voters in Scotland are moving away from Labour and choosing the SNP, and we will continue to work hard to earn people's trust.
"The cuts being proposed by Labour, the Tories and Lib Dems are a huge threat to the public services we all hold dear. That is exactly why we need a big group of SNP MPs in the next House of Commons to achieve real change and an end to austerity - our pledge is to be a strong voice for Scotland, and use our clout to help deliver progressive politics across the UK."
Ms Sturgeon further commented on the two brief paragraphs in the Labour manifesto dealing with additional powers for Scotland:
"New powers for Scotland rated just two brief paragraphs in Labour's manifesto, and six words by Ed Miliband at the launch - which confirms how low down Scotland is in the priorities of all the Westminster parties. Scotland needs the extensive new powers we were promised during the referendum in the Vow - financial powers to grow our economy, and welfare powers to build a fairer society. And it is abundantly clear that the only way this will happen is if Scotland elects a big team of SNP MPs on 7 May."