The Member of Parliament for Wigan said she believed the party had to change to regain the trust of voters after suffering the huge loss.
Nandy, who served as the shadow Energy Secretary from 2015 to 2016, said she was "heartbroken" to see so many working class constituencies had chosen the Conservatives over Labour at the last general election.
In a stark warning to party members, Nandy, who has championed the needs of Britain's towns, said "unless we change course, we will become irrelevant".
She said the drubbing at the hands of Prime Minister Boris Johnson's Conservative Party, including losing swathes of seats in the northern heartlands, was a "long time coming."
Nandy argued that the next leader should come from those areas which feel neglected and are turning away from the party, with a deep understanding of the problems of the regions face.
"It has been 14 years since Labour last won power and I want you to know I have listened and I understand that we have one chance to win back the trust of people of Wigan, Workington and Wrexham. Without what we were once our labour heartlands we will never win power in Westminster and help to build the country we know we can be.
"I wanted to tell you first that I'm standing to be leader of the Labour Party because after a decade of having the privilege to represent you, I have a deeper understanding of what has gone awry in our discredited political system," she said.
Nandy said the next Labour leader will have to be up for a scrap - willing to run to the places "we are loathed, take the anger on the chin, make and win argument".
She said she was "determined to defeat Boris Johnson in order to lead the compassionate, radical, dynamic government I firmly believe you want and you deserve".
Labour's ruling National Executive Committee (NEC) will set out a timetable on Monday for the leadership campaign. It is thought it will be completed by the end of March.
Corbyn is standing down as leader following the party's crushing election defeat.
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