The former Home Office minister said Labour must not be “afraid” of the argument and had a moral responsibility to talk about immigration reform.
He also said UKIP voters were “darkly pessimistic” about their lives, whereas progressive politics was optimistic.
David Cameron and Ed Miliband clashed on the issue this week – with both attacking the other party’s record.
Official figures published in August showed UK net migration – the difference between those entering and leaving – increased by more than 38% to 243,000 in 2013-14. EU citizens accounted for two-thirds of the growth.
The Labour leader has promised to bring in an immigration bill creating “clear, credible and concrete changes” within months, if Labour wins next year’s general election.
Mr Byrne – Labour’s universities spokesman who was immigration minister in the last Labour government – told Total Politics magazinethe party “can win an argument on this, but we have got to have the courage to put it at the top of our list of things we talk about”.
“And we have got be honest about the realities,” he said.
Perhaps there are some colleagues who feel nervous talking about immigration. I certainly don’t”
Mary CreaghShadow transport secretary
And he cautioned politicians against ignoring voters’ concerns: “If people then sense that politicians are trying to duck the issue or avoid it or not confront it they are just not prepared to have that – and frankly, why should they?”
He expressed confidence that voters backed his proposal to exempt students from migration targets: “People know that students are good for Britain, not bad for Britain, they know that they are critical for our future influence in the world.”
The Birmingham Hodge Hill MP said Mr Miliband had to offer a positive vision to voters who had been attracted to the UK Independence Party: “The curious thing about UKIP voters is that they have one big thing in common: they are darkly pessimistic about themselves and their lives and if you want people to vote for progressive politics, you need people that are optimistic.”
Meanwhile his colleague, shadow transport Sscretary Mary Creagh told The House magazine Labour “needs to acknowledge the strain on schools, public services and the fact that people want to feel that people have put into a society before they start taking something out”.
“We are the Labour Party, we do like talking about the NHS and we are right to talk about the NHS. But perhaps there are some colleagues who feel nervous talking about immigration. I certainly don’t.”
Mr Cameron’s Conservative Party is facing a difficult by-election in Rochester and Strood, Kent, called after one of its MPs, Mark Reckless, defected to UKIP, which campaigns for the UK’s exit from the European Union.
The prime minister has said action is needed to curb EU immigration and has pledged to have “one last go” at negotiating a better deal for the UK in Europe.
There have been reports that the coalition could seek an “emergency brake” to stop EU migration after it reached a certain level or to limit the number of National Insurance numbers issued to new arrivals from the EU.
But German Chancellor Angela Merkel has appeared to rule this out, saying there could not be “tampering” with the EU principle of free movement of people.