Alistair Darling said his side had to "win well" to head off calls for another poll, the so-called "neverendum".
He contrasted the No campaign's position with that of the nationalists, saying they had to win only "by one vote" to achieve their ultimate aim.
At an event with journalists in Westminster, Mr Darling, who heads the Better Together campaign, said: "It is a fact the nationalists only need to win once by one vote and there is no going back – we are all agreed that whatever the independence result is, we will stick to it."
He added: "I do think that we [the Unionists] need to win well because I do not think that it will do Scotland any good to be talking about the constitution year after year while parking big issues like how do we improve our health, our education or our transport, because frankly, lots of big issues are not getting the attention they deserve because so much in Scotland is seen through the prism of the constitution."
But he refused to be drawn on what percentage of the vote he thought necessary to prevent calls for another referendum within just a few years. "I will tell you the day after what number we were aiming for," he said.
Senior Coalition sources said earlier this year that a "crushing defeat" was needed to ensure the independence question was answered for a generation. They warned that if 40% or more of the population backed calls to leave the UK, pressure could build for another referendum within just a few years.
Former Chancellor Mr Darling said his campaign had upended the belief independence was inevitable. He said: "A year ago there was a feeling independence was inevitable, but 12 months later that has changed. The majority of people do not accept the nationalist argument."
The Edinburgh MP also said he had no objection "in principle" to Scottish Labour leader Johann Lamont's proposal to devolve all tax-raising powers to Holyrood, a move which triggered objections from some Scottish Labour MPs.
But he warned that any significant extension of devolution would have to be approved by UK as well as Scottish voters. Mr Darling said: "If you are going to stand on any platform of constitutional change you are duty bound to put it in a UK manifesto."
He refused to be drawn on the comments by former Labour Prime Minister Gordon Brown that the Conservatives were close to adopting Enoch Powell-style rhetoric on immigration.
In other remarks, Mr Darling attacked calls for RBS to be split up as "ridiculous". He warned that such a move would leave taxpayers with the "bad" part of the bank "while someone else walks off with the good bit".