Labour's Jackie Baillie had called for this to be a key part of legislation going through Holyrood, which sets out how such ballots would take place.
With Constitutional Relations Secretary Mike Russell and First Minister Nicola Sturgeon both backing a so-called People's Vote on Brexit, Ms Baillie said the same principle should also be applied if there was to be a second vote on Scottish independence.
She put forward an amendment to the Scottish Government's Referendums Bill to achieve this - which was rejected by nine votes to two by MSPs on the Finance and Constitution Committee.
They voted down Ms Baillie's amendment after the Constitutional Relations Secretary argued the legislation was designed to cover all possible future referendums and did "not seek to prescribe different referendum processes for particular subject matters".
Mr Russell said "automatic second referendums are not required", although he did accept there could be case for them in situations such as the 2016 European referendum "where the information provided to voters was flawed" or "where circumstances have changed, where things are no longer what they were".
Ms Baillie said she was "disappointed" the Scottish Government had not backed her amendment "given the very fulsome comments from the First Minister and the Cabinet secretary about a People's Vote".
She argued: "I do think it is slightly hypocritical to make the argument a second confirmatory referendum is required in the case of the EU, while at the same time insisting a major constitutional change in Scotland's status in the UK, in a much longer established union, wouldn't require that."
'Holding referendums to a higher standard'
The Labour MSP added: "Major constitutional issues, in my view, require consent based on what it would mean rather than a vague notion of simply taking back control.
"I would much rather run the risk of voter fatigue on substantial issues of constitutional change than make a change which would harm the country without consent."
With the committee considering the detail of the Referendums (Scotland) Bill, Scottish Greens co-leader Patrick Harvie made a call for the law to be changed so it would be an offence to make false statements during a referendum - as it already is during election campaigns.
"If we are going to have more referendums in Scotland in the future we should hold them to a higher standard," he said.
Mr Russell said while the Green MSP has raised an "important issue" he could not support such changes to the legislation.
He warned the committee: "Regulating the truthfulness of campaign statements cannot be done effectively at this stage and cannot be done by these amendments.
"The likely outcome of this approach would be severe curtailment of freedom of speech."
Mr Harvie withdrew his amendment
Mr Harvie withdrew his amendment but said he would "consider if there is another way to bring this debate to the chamber".
Conservative MSP Adam Tomkins also put forward an amendment that would, if passed, have required ministers, the Scottish Parliament, MSPs and public bodies to "respect decisions made by referendums".
He said: "I suppose it is an attempt to prevent referendums becoming what the Canadians once called 'neverendums', that referendum outcomes are somehow not determinative of the question which have been put to the people."
But he did not press this to a vote after Mr Russell told the committee that as referendum results were "not always clear cut" there "needs to be space" for politicians to consider how to move forward.