Leader Johann Lamont was speaking in the constituency yesterday, hours after her party's thumping two-to-one victory over the SNP, taking a 56% share of the vote to their opponents' 28%.
She said: "It's a very significant result and I believe people in this area have responded to our positive campaign on jobs, education and support for older people.
"These are the issues they want politicians to be focusing on, and that's what Alex Rowley will be doing as an MSP. I think voters are telling Alex Salmond to get on with his day job."
Mr Rowley said: "The priorities I have are the things that came up on the doorstep time and time again; unemployment, youth unemployment, giving young people the best chance in life, tackling a housing crisis in the top side of this constituency."
Given a slightly disappointing turnout of 34.78% it was a terrific night for Labour, a poor night for the SNP, a decent night for the Tories, a pleasing night for Ukip, and a shocker for the party pushed into fifth place, the Liberal Democrats.
SNP strategists openly talked about how the mid-term effect in this session may be taking them back to where they were in 2007, but they insist the party is doing well.
The seat has been vacant since the death of Labour MSP Helen Eadie in November last year, just days after it emerged she was being treated for cancer. Mr Rowley has for a year been an aide to former Prime Minsiter Gordon Brown, and he pledged to stand down as leader of Fife Council.
He has faced bitter disappointment in the past, particularly in 2011 when he expected to take back Dunfermline from the Liberal Democrats only to lose the seat unexpectedly to the SNP.
Natalie McGarry, who came second with 5704 votes, said: "I am confident that there will be a Yes majority in September. I heard on the doorsteps from a lot of traditional Labour voters who said: 'Listen, Natalie, I'm not going to vote for you, but I am actually thinking about voting Yes in the referendum.'"
Ms Lamont dismissed Ms McGarry's comments, saying: "I think we've got to a stage ahead of September where we don't believe a word the SNP say about anything.
"I think they maybe need to stop talking to each other and listen to what people in the real world are saying about their concerns."
SNP business convener Derek Mackay MSP insisted the result indicated the party's underlying strength in Scotland, with a share close to that in 2007 when the SNP won.
"The SNP fought a strong campaign with an excellent candidate in Natalie McGarry and we made the issues of the by-election the issues that matter to the people - the council-tax freeze, free school meals and extending childcare," he said.
Local councillor Dave Dempsey, who came third for the Conservatives with 1893 votes, achieved one of the surprise results in Thursday's poll. He said: "You could not buy the effort, dedication and enthusiasm that I have had at my disposal over the last several weeks. We're getting there."
He had a point. The Tories were the only party to increase both their percentage share and number of their vote while on a reduced turnout everyone else's was falling.
Denise Baykal came fourth for the UK Independence Party (UKIP) with 610 votes while Jade Holden was in fifth place for the Liberal Democrats with 425 votes.
Liberal Democrat leader Willie Rennie put a brave face on a terrible result in the home constituency where he was raised, saying of his candidate: "In a crowded two-horse race Jade made her voice heard on Liberal Democrat commitments for lower taxes, higher pensions and more jobs.
"This is the positive message which we are taking to the Scottish voters."