The shadow Home Secretary, who was born in Inverness, also said she was “worried” by the Tories decision to play the anti-Scottish card using the fear of the SNP in the election and warned it would happen in the future as well.
She also called for a written constitution to help bring the UK back together.
In answer to another question, Ms Cooper also made a thinly veiled attack on the wives of leading male politicians including Samantha Cameron and Ed Miliband’s wife Justine Thornton who join their husbands on the stage after a conference speech.
She said it was time politics moved on and insisted her famous political husband Ed Balls will not be joining her on stage.
She said: “I told him [when he ran for the Labour leadership in 2010] that I wouldn’t join him on the stage as a political wife so I think it would be a bit much for me to ask him to do it.”
But she said she felt “deeply uncomfortable” about the way wives were still expected to join their political husbands on the stage.
But Ms Cooper saved her toughest message for dealing with the SNP and made it clear that under her leadership there will be no deal of any kind with the Nationalists.
She said: “I don’t think you can have any kind of agreement with a party that wants to separate a country or fracture a country in that way.”
Attacking the Tory “English nationalist” election strategy, she went on: “I do feel quite worried about the way in which about the way David Cameron had decided to play that politics.”
“I feel worried about the careless way in which David Cameron thinks it is OK to play on the fear of Scotland as being the way for them to get more votes and the way in which that divides a nation.”
She added: “I think that they [the Tories] will continue to do this and it’s a real challenge for the Labour Party for us to try and build that sense of things that we have in common rather than things that pull us apart.”
She suggested that a new written constitution for the UK with the shared values of its nations might be the way forward.
She said: “I think we need to reconsider having a written constitution because you got you can see our written constitution now being stretched to the seams and we need to talk about the values we share.”
But she admitted it is “a long hard road” for her party to recover north of the Border.