The Labour leader said that when the party 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".
He added: "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."
More top news
New security checks for travellers heading to France cause tailbacks of up to 20 hours for some.
More than 11,000 BHS workers will be told they face redundancy consultation today.
Divisions among MPs and party supporters have intensified in recent weeks amid an increasingly fraught leadership battle.