The Opposition leader said the previous Labour government had become distant from the public on issues such as immigration, and failed to rein in excess at the top of society.
Miliband said Labour didn't do enough to stop 'rampant free markets'
Fleshing out his vision of One Nation Labour in a speech to the Fabian Society, he also highlighted new policies designed to help people priced out of buying homes.
It is Miliband's latest attempt to distance himself from elements of the last government's record considered toxic by many strategists.
New Labour was "too timid in enforcing rights and responsibilities, especially at the top, and it was too sanguine about the consequences of the rampant free markets".
He said: "By the time we left office too many of people of Britain didn't feel as if the Labour party was open to their influence, or listening to them," Miliband said.
"For me, the most obvious example is immigration. I bow to nobody in my celebration of the multi-ethnic, diverse nature of Britain. But high levels of migration were having huge effects on the lives of people in Britain - and too often those in power seemed not to accept this.
"The fact that they didn't explains partly why people turned against us in the last general election.
"We have to move on from New Labour, as well as from this Government."
Miliband told the event in central London that if Labour wins the next general election it would have to find ways of achieving change while tackling a lingering deficit.
"One Nation Labour has learnt the lessons of the financial crisis. It begins from the truth that New Labour did not do enough to bring about structural change in our economy to make it work for the many, not just the few. It did not do enough to change the rules of the game that were holding our economy back."
A member of the audience studies paperwork before Miliband's speech
During a question and answer session, Miliband spoke to an audience member who stood as a parliamentary candidate for the party in 1951.
After being told that Labour's slogan then was "Fair Shares for All", Miliband said: "That's very One Nation ... We might use that."
Detailing his concerns about the housing market, the Opposition leader pointed out that 3.6 million households, including one million with children, are now in privately rented accommodation. The numbers are bigger than in the social rented sector for the first time in almost half a century.
"We cannot have two nations divided between those who own their own homes and those who rent," Miliband said.
"Most people who rent have responsible landlords and rental agencies. But there are too many rogue landlords and agencies either providing accommodation which is unfit or ripping off their tenants. And too many families face the doubt of a two-month notice period before being evicted.
"Imagine being a parent with kids settled in a local school and your family settled in your home for two, three, four years facing that sort of uncertainty.
"We would introduce a national register of landlords and greater powers for local authorities to root out and strike off the rogues.
"We would end the confusing, inconsistent and opaque fees and charges regime, making fees easily understandable, upfront and comparable. And we will seek to remove the barriers that stand in the way of longer-term tenancies."
A Conservative spokesman said: "The public deserves better than this. Not once does Ed Miliband answer the tough questions, like how he would deal with the record deficit his Labour government left behind.
"Instead of facing up to the difficult decisions, all Labour offer is more spending, more borrowing, and more debt: exactly how they got us in to this mess in the first place."