Johnson, a former shadow chancellor under Miliband, also said trade unions were in danger of becoming irrelevant and should have less power in the Labour party.
Many unions "cannot connect to a whole swath of the workforce that thinks they died out with the ark", he said in an interview for Progress magazine.
One reason was the image of "fat, white, finger-jabbing blokes on rostrums shouting and screaming", Johnson said, and the only sign of "rational thought" in the union movement came from the Trades Union Congress rather than individual unions.
Johnson praised the decision of Ed Miliband and Ed Balls last year to back the coalition's multi-year public sector pay freeze, a decision "in which they almost invited the hostility of the trade union movement, and got it, from Len McCluskey".
"For the first time I felt we were living in the world of 2015 not 2010," he said.
Asked whether Labour should commit to sticking to the government's spending limits for the first two years if elected – as it did in 1997 – Johnson said it was "difficult to think what else you can do".
"We can't get away from the fact that the fiscal deficit has got to come down," he said.
"Now is a dangerous time. We can't get away with saying we are thinking about policy. That's perfectly acceptable for the first three years, but now we have got to start unveiling some policy and what Ed's going to need to do is to meet the expectations he himself has created."
In an interview for the BBC's Andrew Marr programme, Tony Blair said he did not think there was a need yet for detailed policies. "They're an opposition party. So I don't favour as an opposition party, you know, hugely detailed policy, but the orientation's going to be clear," he said.
Speaking to Sian Williams, who was standing in for Marr, Blair said: "I think what there will be is a big challenge when it comes to how do you translate that vision into practical policy, and that's for later in this year when the Labour party will start to unveil its policies.
"We're going to face the situation – whoever's in government – where they're going to be very constrained, and that's why it will be important for the Labour party to show they are reformers and they're able to reform public services, welfare, the state and so on as well as simply protect people who are vulnerable."
In the Progress interview, Johnson called for more working-class MPs in parliament but said this should not be "left to a small clique in the affiliated unions who want to get the people who mirror their views into parliament".
Johnson singled out McCluskey, the Unite general secretary, for urging the "Blairite cuckoos" to be "kicked out of the nest".
"So Len McCluskey says kick the Blairites out, the people who introduced the national minimum wage; introduced the right to six weeks' paid holiday; introduced the right to trade union representation [and] whistleblower legislation; ensured that part-timers got the same [rights] as full-timers; upped maternity leave from 14 weeks to nine months; introduced paternity leave for the first time ever; got rid of discrimination on the grounds of sexual orientation. I mean, you can go on for ages. Talk about what did the Romans ever do for us?"
Decrying an absence of fresh thinking, the former home secretary warned the unions: "You have only got 6 million members. When are you going to start addressing the real problems you have got?
"With 6 million members not 13 million members … it is becoming increasingly difficult to defend things like defined benefit pensions in the private sector. [The unions] did a brilliant job defending them in the public sector, and that's good, but ... the danger is that they become irrelevant.
"If I were the trade union movement I would be coming to the Labour party saying: 'There is no earthly reason why we should have 50% of the conference vote' … We'd be coming forward as comrades saying: 'On the national policy forum it's about a third of the vote with trade unions, that is about where it should be.' I would be coming to the party saying: 'This is what we want to do, be bigger and healthier.'"
Johnson said the next election could have the feel of a "postwar election, thankfully without the carnage, where people are saying 'we are not going to go back, whether it's hacking, or bankers' bonuses, or what was happening in financial services'."
This presented a "huge opportunity" for the left, he said, and, citing the Labour leader's 2011 "predators versus producers" party conference address, he argued that Miliband was right to adopt this agenda.
However, he said, people wanted "an awful lot to change and Ed could have played it safe, but he hasn't, and the question people now ask is: 'How are you going to do all of this?'"
Johnson said the Tories' poll lead over Labour on the question of who could best handle the economy was gradually eroding, but conceded: "I don't know whether we've got the message across as effectively as we could."
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