The final contenders for the Labour leadership have answered questions at a hustings in Glasgow, with all three backing more powers being devolved.
All three MPs agreed that the party had to win in Scotland to win back power.
However, Ms Long-Bailey was the only one to explicitly state she would agree to a fresh ballot on independence.
She insisted her party must not “fall into the trap” again of working with the Tories to try to keep Scotland in the UK.
The shadow business secretary and her fellow leadership hopefuls, shadow Brexit secretary Sir Keir Starmer and former shadow climate change secretary Lisa Nandy, became the final three contenders in the running to succeed Jeremy Corbyn after Emily Thornberry was eliminated for failing to secure enough nominations before the deadline on Friday night.
At the SEC in Glasgow, the remaining contenders all stressed the importance of Labour winning back support in Scotland as a route back to power across the UK.
Ms Nandy said: “There is no route to government that doesn’t run through Scotland, but the challenge of this is absolutely enormous.”
She added: “We have to start winning in every region and nation of the UK, because we have to show we are a national party of government.”
Similarly Sir Keir said: “We can’t win without Scotland so we have to rebuild in Scotland.”
Ms Long-Bailey – an ally of the departing Jeremy Corbyn – also echoed that, telling activists at the event: “We won’t win a general election without Scotland.”
Asked directly if the Scottish Parliament should have the power to stage a legally-binding vote on independence, Ms Long-Bailey reiterated that while she is opposed to independence she does not think Westminster should block indyref2 against Holyrood’s wishes.
On Saturday she said: “I’m proud to be from the United Kingdom but as a democrat I have to say that if the Scottish Parliament makes the request for a referendum I don’t believe that as a democratic party we could refuse that.”
Her comments came after MSPs at Holyrood voted by 64 to 54 last month in favour of a second independence referendum taking place.
If there is a second vote on Scottish independence she said Labour could make a “positive campaign” for the union.
But she was clear: “We can’t fall into the trap we did last time where we joined forces with the Conservative Party on Better Together.”
However, Sir Keir – who is the bookmakers’ favourite to replace Mr Corbyn – said that by backing a second independence vote Labour could be falling into a “trap” set by the SNP.
He said the issue of Holyrood having the power to stage a fresh ballot on the issue was “an interesting question” but he added: “We shouldn’t get sucked straight into that.
“The SNP are constantly using the constitutional issue to mask the real issues, and if we get into that we are falling into their trap.
“Let’s have a wide discussion about where we go next, but let’s be bold about it.”
He argued that Labour should support “radical federalism as the way forward” for the UK.
Meanwhile, Ms Nandy said she believed in a “much more radical power settlement than federalism with power pushed out to local authorities”.
She told Labour Party members: “I believe in the United Kingdom and I think we have to be absolutely clear about that and we have to stand up for Scotland remaining in the United Kingdom.
“We can hand power to people and give people agency and control over their own lives again by handing more powers to our councils.”
Current leader Jeremy Corbyn confirmed he would step down at his election count in December as his party faced its worst performance in terms of seats since 1935.