Shadow business secretary Ms Long-Bailey launched her campaign with a speech in Manchester, in which she said her party did not talk enough about “aspiration”.
She also vowed to “shake up” the way government works, and put power into the hands of voters.
Described as a “continuity Corbyn” candidate said to be favoured by the current leadership and backed by campaign group Momentum, her supporters have bridled at the description.
As she took to the stage at the Museum of Science and Industry, some of the 300 or so supporters at the event broke into a chant of “Oh Jeremy Corbyn”.
Ms Long-Bailey told them: “Hey guys, we’re going to have to think of a new song you know. No pressure.”
When was asked why Labour had failed with voters, returning their worst electoral result since 1935, she said: “I think for me we had some fantastic policies, I know because I helped write some of them, and really the message didn’t resonate with our voters. And what we should have been talking about is aspiration.
“Because everything we are trying to build and I am going to try to build as leader of the Labour Party is about realising the potential, truly realising that quality of life increase, whether you are a business, whether you are an industry or an individual, our role as a party is to improve your living standards and the wealth you can accumulate as communities.
“And we didn’t say that. We didn’t match that with a message of aspiration. We want an economy where everyone does well.”