LONDON - Johnson, who led the campaign to take Britain out of the European Union, said "hysteria" had gripped those who had supported staying in the bloc, and the government needed to explain the truth about the impact of Brexit.
"There is, among a section of the population, a kind of hysteria, a contagious mourning of the kind that I remember in 1997 after the death of (Diana) the Princess of Wales," Johnson wrote in the Daily Telegraph newspaper.
"It was wrong of the Government to offer the public a binary choice on the EU without being willing - in the event that people voted Leave - to explain how this can be made to work in the interests of the UK and Europe. We cannot wait until mid-September, and a new PM."
The flamboyant and popular Johnson, one of the most prominent Brexit campaigners, had been expected to join the contest to be the new Conservative leader after Cameron announced he would quit following the referendum vote to leave the EU.
However, he pulled out when his ally, Justice Secretary Michael Gove, decided to run for the job himself, calling Johnson's abilities into question, which Johnson's supporters described as an act of Machiavellian treachery.
A new leader is expected to be in place by early September.
Johnson said fears about the impact of leaving the EU had been wildly overdone, saying the stock market had not collapsed and the emergency budget with spending cuts and tax rises had not materialised as finance minister and Remain supporter George Osborne had warned.
Conservative lawmaker Ben Wallace, who was running Johnson's campaign, said he thought Gove himself was unfit to be the leader himself, calling him a gossip. "Michael seems to have an emotional need to gossip, particularly when drink is taken, as it all too often seemed to be," Wallace wrote in the Telegraph.