Angela Rayner also insisted people in Scotland should not “leave behind” those in areas such as Manchester and condemn them to “perpetual Conservatism”.
She made the comments at Iain Dale’s All Talk show at the Edinburgh Fringe on Monday.
Elsewhere, Ms Rayner said Labour was still failing to communicate “the detail” of what Brexit means to the public.
The MP for Ashton-under-Lyne in Greater Manchester also said “so many” Tory Cabinet members “haven’t got a clue” about the financial challenges a lot of people struggle with.
And she said many working-class politicians have their accents “beaten out of them, almost” because of the criticism they receive for it.
Ms Rayner was asked about Scottish independence and working with the SNP by a member of the audience at the Pleasance festival venue.
She said: “It’s not a possibility that we’d work the SNP – we want to win a majority.
"And I don’t think the people of Scotland should leave behind the people of Ashton-under-Lyne either in Manchester, because the poverty we face is the poverty they face and we both need a Labour Government in order to make the changes that we need to make, whether that’s in Scotland or whether that’s in England or other areas.”
She said Labour was “making progress” in Scotland, adding: “I think breaking up the Union is not the answer.
"I think leaving us to perpetual Conservatism in Westminster is not very nice.”
Ms Rayner said having a Labour Government in Westminster “could make all the difference”.
She argued Labour “has been behind on devolution” despite legislating for it, but insisted “really engaging with devolution could be the key”.
She said: “I’m against us going anywhere near a second referendum, if I’m honest.
"I think the Brexit referendum was enough for me, thank you very much.”
Put to her that this position disrespected those who voted for a pro-independence majority in Holyrood, Ms Rayner said: “I wouldn’t say it’s me showing disrespect.
"I’d say it’s me being honest as a politician with people.
"I think you can disagree with me on that position, and that’s completely fine.
"But I think one of the things that is a problem in politics is when you try and triangulate.
"I think it’s better for Scotland, and I think it’s better for my constituency, that we’re part of the Union.
"But I think it’s also equally important that we don’t have the Conservatives in power in Westminster.
"I think that is the biggest damage that’s being done to Scotland.”
She added: “If we ended up in Government there would be a huge difference in what happens in Scotland. Real devolution, real respect.”
Ms Rayner said real devolution meant “working together” on issues such as renewable energy and building the economy.
She said: “I think a Labour Government in power in Westminster could make a massive difference to Scotland, and I think it could make a massive difference to Manchester.”
The event at the Edinburgh International Conference Centre was later briefly disrupted by environmental campaigners asking about a “green new deal”.