Ed Miliband has insisted it is "understandable" that people are worried about immigration as he promised to win back voters from Ukip.
After Nigel Farage's party made significant gains in key Labour areas, Mr Miliband admitted that the concerns of working families on the issue had been neglected.
But he warned that Ukip's approach of blaming "Europe and foreigners" for the country's problems was "not the answer".
The comments came as Mr Miliband visited Thurrock and took questions from local people. The Essex town is a key target seat for the general election, but Labour failed to win control of the local council last week due to Mr Farage's surge.
Mr Miliband argued that results in the European and local polls had to be viewed in the context of economic, social and political upheaval over the last three decades.
Although the last Labour government achieved much to help families, it had not been "enough".
"Our embrace of the future meant that some people thought we didn't respect the loss they felt from the past," he said. "Our embrace of openness made some people feel we didn't understand the pressures immigration put on them.
"Our embrace of economic change, on the one hand, and our determination to do right by the very poorest, on the other, led people to believe that we didn't care enough about ordinary working people."
He said Ukip had managed to "exploit" that alienation to boost its support.
"Labour was founded on standing up for working people. But for too many that link was lost," he said.
"That is what Ukip has sought to exploit.
"We know what their appeal is. They provide a simple explanation of the cause of our country's problems: Europe and foreigners.
"And they have an apparently simple solution: to get out of the European Union.
"I have to say: this is not the answer for our country, this will never be Labour's mission or policy under my leadership. Our future lies in looking outward to the world."
Mr Miliband said he was proud to be the son of immigrants, and believed immigration had "benefited our country as a whole".
"But it needs to be properly managed," he added. "I have changed Labour's position on immigration since 2010.
"It is not prejudiced to worry about immigration, it is understandable.
"Labour would have controls when people arrive and leave here, we will tackle the undercutting of wages, we will ensure people in public services speak English and people need to earn their entitlements.
"But a Labour government won't make false promises, or cut ourselves off from the rest of the world because it would be bad for Britain."
Answering questions from local party members and journalists during a Q&A session, Mr Miliband said: "It's not right-wing for us to talk about immigration, it really isn't.
"We have got to be willing as a party to talk about immigration.
"We can talk about it in a progressive way."
Mr Miliband said there was a need to stop wages from being undercut and to tackle recruitment agencies who only look for workers overseas.
He added: "I totally understand the anxiety there is in the party about talking about this.
"But if we don't talk about it and we let Nigel Farage talk about it or David Cameron talk about it then we are not going to have it talked about in the right way."
Asked about an in/out referendum on the EU, Mr Miliband said: "I think it's important to say that the EU has got to change.
"You have got more than 20 million people out of work across the European Union, you have got millions of young people out of work across the European Union, and you have got a sense - and you saw it in these results - that the EU doesn't work for people.
"The best and most important thing the Labour Party can do is own that change and say 'we do want to change the way the EU works'.
"But does that mean we should get out of the EU? In my view, no."
He said that "people are smart" and know that many jobs depend on remaining part of the EU.
Mr Miliband was also asked about the referendum on Scottish independence, which he described as "existential" for the country.
"We have got to win this referendum an we will win the referendum in my view," he said.
He claimed "social justice" would suffer with Scotland outside the UK.
"Why is Alex Salmond's first promise for an independent Scotland a 3p cut in corporation tax?
"It tells you quite a lot about where his agenda is and what his priorities are.
"So it's a referendum we've got to win and all of us in England as well as in Scotland has to be part of that referendum, has to be saying we want Scotland to stay.
"Not just Scotland is better off staying in the United Kingdom but the whole of the United Kingdom is better off with Scotland in it."