Nicola Sturgeon has said securing a legally-binding referendum is a "hard truth" to accept for some independence supporters.
The first minister said she was working to get the powers to hold another vote transferred from Westminster.
But she conceded there are some independence backers who want a Catalan-style unauthorised vote.
Opposition parties have repeated their calls for Ms Sturgeon to drop demands for another referendum.
The SNP leader has said she will submit a formal demand to the next UK government to give consent to another independence referendum, known as a Section 30 order, immediately after the general election.
In 2014 temporary section 30 powers were passed to the Scottish Parliament to hold a legal referendum.
Speaking on BBC Radio Two's Jeremy Vine show, she said: "I am in the business of winning Scottish independence, not just having a referendum to make a point or have a gesture.
"No matter how difficult this seems sometimes, you have to have a process that is legal, that is constitutional and that is capable of being accepted not just within the UK but within the EU.
"For those who want Scotland to be become independent that, at times, can feel like a hard truth, but it is a truth nonetheless."
Ms Sturgeon added that if a legal deal could be agreed in the run up to the 2014 referendum then there was no reason why this could not be repeated.
However, interim Scottish Tory leader Jackson Carlaw has claimed Scotland would "sleepwalk into disaster" if voters backed the SNP or Labour in the general election.
He said Jeremy Corbyn would "cave in immediately" to the first minister's demands for a second vote on independence if SNP MPs help him into Downing Street in the event of a hung parliament.
Mr Carlaw called on Scots to act to deny the SNP that "bargaining power".
Scottish Labour leader Richard Leonard has said he is opposed to Scottish independence but added that a UK Labour government would not block a future referendum if there was "demonstrable" support in Scotland.
Lib Dem leader Jo Swinson has said another referendum would bring "extra chaos" and has said she would block any move for a second vote.