Speaking on the eve of the party’s annual conference, the former foreign secretary said Labour had “no strategy” for Britain’s withdrawal from the EU.
The issue is expected to dominate the gathering in Liverpool, with Jeremy Corbyn facing mounting pressure to support a public vote on whatever deal Theresa May negotiates with Brussels.
Grassroots activists hope to use the conference to force a change in policy towards backing a final say referendum.
It comes after Theresa May admitted negotiations were at an “impasse” and warned that the UK would leave the bloc without a deal unless EU leaders agree to compromise.
Mr Miliband, a former Labour leadership candidate, told BBC Radio 4 Today: “Labour has got to be much, much stronger. The truth is that waiting for the government to foul up is no strategy at all. The country desperately needs a strong government but it also need a strong opposition.
“Labour’s tragedy over 20 years – and I include my own period in this – is that there was almost a complacency about Europe. The Tory tragedy was to be obsessed about Europe and the Labour tragedy was to be complacent about Europe.”
He added: “Finally the complacency is breaking, at least at the constituency level of the Labour Party, but it’s an absolute dereliction of duty for the Labour Party leadership not to embrace the fundamental principle that since the Brexit that people were sold two years ago is not available, it’s essential that the Brexit deal the prime minister does is put to people.
“The most corrosive thing in the long term will be a Brexit on terms that were missold.”
Mr Miliband predicted Ms May would “eke out” a “paper-thin deal” with Brussels and then “use the threat of no deal and the disaster that represents to try to bludgeon people to support it”.
He said: “No-deal is obviously a terrible disaster for the country.
“Theresa May has painted herself and painted the country into a corner. We’re now in a situation where the contradictions and the delusions of Brexit are coming home to roost. There is no Brexit where you can have the benefits of the European Union without living by their rules.”
But speaking to Today, Dawn Butler, the shadow women and equalities minister, defended her party’s handling of Brexit.
She said: “Labour has been absolutely clear and steadfast from the very beginning.
“[Shadow Brexit secretary] Keir Starmer and his Brexit team looked at all of the paperwork in detail and from that he developed six tests, and from that he talked about having this relationship with the customs union.”
She added: “If Theresa May brings back a deal that doesn’t meet our six tests, we will not vote for it. We’ve been very clear about it.”
Ms Butler said Labour wanted to see a general election rather than another referendum.
She said: “Our priority is making sure that we are not worse off – that we have a jobs-first Brexit, that we protect the rights of people in our country and services for people in our country.”