Mr Johnson's attack comes after his call for a general election was defeated in the Commons.
But Labour and other opposition MPs refused to back the bid - which needed a two-thirds majority in the Commons - while the risk of a no-deal remained.
The Government failed to secure the support of two-thirds of MPs, with the Commons voting 298 to 55. That falls 136 short of the number needed under the Fixed Term Parliaments Act for a vote to be considered.
It's his third defeat in 24 hours; by comparison Tony Blair lost four times in a decade of leadership, Margaret Thatcher lost same number of times in eleven years of holding office.
Johnson hits out at opposition over election backing
In an with ITV's Peston programme, following 24 hours which saw his government defeated successive times, Mr Johnson said: "I'm afraid what we've heard from the Leader of the Opposition today is not only does he want to cancel the referendum.
"Not only does he want to extend the UK's membership of the EU, at the behest of the EU, giving that power to keep us in potentially for years and years at their own discretion."
He continued: "But also he now refuses, contrary to what I think is the constitutional duty of a Leader of the the Opposition, he refuses to take part in a general election.
"I don't think I have, I have never known a time in modern history when the Leader of the Opposition has refused to take part in a general election.
"I can only invite our viewers, Robert, to speculate why he may be so disinclined - does somebody need to get out the chicken suit?"
Labour and Lib Dems refuse to back Johnson's election
Both Labour and the Liberal Democrats said they would not back the motion until chances of a no-deal Brexit were taken off the table.
Mr Corbyn said the bill must be passed through the Lords and have received Royal Assent before he would entertain the thought of a general election.
Tweeting after the results of the general election vote, Mr Corbyn added: "When no-deal is off the table, once and for all, we should go back to the people in a public vote or a general election to decide our country’s future."
Birmingham Yardley MP Jess Phillips told ITV's Peston programme she would "rather look like a fool and protect my constituent’s jobs" than back a general election and see the country leave the EU on a no-deal ticket.
Turbulent day in Commons sees Government passed and motion passed by default
Video report by ITV News Political Correspondent Paul Brand
In a series of setbacks, MPs also approved a backbench Bill earlier in the evening to delay Brexit in order to prevent a no-deal withdrawal from the EU on October 31.
It cleared the Commons when it passed its third reading by 327 votes to 299, majority 28, and should now progress to the Lords.
Following a moment of confusion, an amendment seeking to give MPs a vote on Theresa May's final Brexit deal was also passed - potentially paving the way for it to be put before the Commons for the first time.
Labour MP Stephen Kinnock's amendment was approved after tellers for those voting against the amendment were not put forward during voting.In his response Johnson says Jeremy Corbyn is the first opposition leader in the history to refuse an election.
A Government source said it was a "free vote so no-one put tellers in".
Mrs May's final offer, the Withdrawal Agreement Bill, emerged from cross-party talks earlier this year, but was never put before Parliament because she stood down as Tory leader.
Tory deselection before a proposed election fallout continues
During his exclusive interview with Robert Peston, the prime minister said removing Tory MPs from the party gave him "no joy" but they were aware of the consequences of not standing by the Government.
He told Peston: "These are friends of mine. Believe me, I take absolutely no joy in any of it. But it was very sad and surprising that they should chose to undermine the UK's ability to get a deal - that's what it does.
"I think what the country wants to see if clarity and determination in coming out of the EU on October 31.
"And alas, for those colleagues who have plenty of warning and explication about backing a bill, the surrender bill, that effectively frustrates Brexit - we made very clear to them what the consequences are."
The former attorney general, and now deselected MP, Dominic Grieve said he hasn't formally been told he's no longer part of the party - but has been removed from party Whatsapp groups.
David Gauke also chipped in on the debate, writing on Twitter his party membership is still valid but he is barred from being reselected to represent it at at forthcoming general election.
Watch Robert Peston's full interview with Prime Minister Boris Johnson