The Prime Minister said he wanted to head to the polls next month to break the political deadlock, as he accused opposition parties of making "outrageous excuses" to delay.
-> Tories destined for election failure with Boris Johnson’s hard line: Andrew VineBut 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.
MPs voted 293 to 46, short of the 434 needed - marking the new PM's sixth Commons defeat.
The prorogation, passed in the early hours of Tuesday, makes a general election extremely unlikely until at least mid-November.
Parliament was suspended for five weeks around 1.45am following a ceremony interrupted by protests from opposition MPs, bringing to a close the longest parliamentary session in the history of the UK.
Signs bearing the word "silenced" were held by some Labour MPs, while Lloyd Russell-Moyle appeared to try to hold on to Mr Bercow at the point he was requested to lead MPs to the Lords.
Shouts of "shame on you" could be heard as Government MPs left the Commons to head to the House of Lords for the prorogation ceremony.
-> Claims I'm about to quit as Minister are wide of the mark, says Yorkshire MP Julian SmithEarlier, Mr Johnson, who on Tuesday was expected to continue campaigning for the election he is yet to successfully call, said Jeremy Corbyn had become the first leader of the opposition in the country's history to "show his confidence" in the Government "by declining the opportunity to have an election with a view to removing the Government".
But amid stormy scenes in the chamber Mr Corbyn said he would not let his party walk into "traps laid by this Prime Minister".
"This Government is only interested in shutting down Parliament to avoid any scrutiny," the Labour leader said.
-> Labour will be punished by northern voters if it backs staying in the EU, says outgoing MP John MannThe PM insisted he would not ask for another Brexit delay, despite royal assent being given to legislation requiring an extension to the UK's EU membership unless a divorce deal is approved or Parliament agrees to leaving the EU without one by October 19.
Mr Johnson said: "It's plain from the turbulent reaction of the benches opposite that they simply want another delay and I will not have that.
"I must warn members that their behaviour in thwarting the will of the people is undermining respect for this House in the country.
"If honourable members want a delay, the only proper way to do it is to ask permission from our masters the people, from our masters the voters."
Following the defeat, Mr Johnson said the Government would "press on with negotiating a deal while preparing to leave without one" ahead of the European Council summit on October 17.
The Prime Minister said: "No matter how many devices this Parliament invents to tie my hands I will try to get an agreement in the national interest.
"This Government will not allow Brexit to be delayed any further. While the opposition run, they cannot hide forever."
-> Claims I'm about to quit as Minister are wide of the mark, says Yorkshire MP Julian SmithIn a day of high drama in the Commons in which the Speaker John Bercow announced his intention to stand down next month, MPs also demanded the Government publish communications connected to prorogation and no-deal Brexit planning.
Former attorney general Dominic Grieve's demand for all written and electronic contact about the temporary suspension of Parliament and Operation Yellowhammer documents since July 23 to be released was approved by 311 votes to 302, a majority of nine.
Meanwhile, Mr Johnson will continue campaigning for an election when he visits a primary school in London on Tuesday to mark the launch of an education drive which could see up to 30 new free schools established.