Commenting on the result, Keir Starmer said: "This is a disappointing, narrow defeat".
If passed the motion would have would allowed MPs to take control of the House of Commons agenda - which is normally in the hands of the Government - on Tuesday 25 June.
The Labour MP backed her party's efforts to take control of the parliamentary agenda, allowing it to table legislation to thwart the United Kingdom leaving without any agreement on the October 31 deadline.
Tory leadership frontrunner Boris Johnson said that he was "not aiming for a no deal" but that MPs would "reap the whirlwind" if they tried to thwart Britain's withdrawal from the EU.
The procedure is the same as one used by opposition MPs to block a no deal Brexit before the 29 March deadline. "But this is just the start, not the end of our efforts to block no deal", he said.
"He has been around in politics for a while, he has achieved a lot, he has still got a big role to play, but I think if we are trying to connect with the next generation and move forward as a country, then I think it is time for the next generation with a bold new agenda".
"I think if we now block it, collectively as parliamentarians we will reap the whirlwind and we will face mortal retribution from the electorate".
"It is only responsible to prepare vigorously and seriously for no-deal", he said.
"Any Tory leadership candidates should know that Parliament will continue to fight against no deal".
Labour used its opposition day debate to present a motion created to hand over control of the parliamentary agenda on Tuesday 25th June to MPs.
"Around the country there is a mood of disillusion, even despair, at our inability to get things done", he said.
"After three years and two missed deadlines we must leave the European Union on October 31".
Those Labour MPs who rebelled to oppose the motion included Sir Kevin Barron (Rother Valley), Ronnie Campbell (Blyth Valley), Jim Fitzpatrick (Poplar and Limehouse), Caroline Flint (Don Valley), Stephen Hepburn (Jarrow), Kate Hoey (Vauxhall), John Mann (Bassetlaw) and Graham Stringer (Blackley and Broughton).
Sajid Javid, one of the candidates vying to succeed British Prime Minister Theresa May, said his rival Boris Johnson was "yesterday's news" and that it was time for a new generation to take control of the Conservative Party.
"No-deal can not be imposed on the country or on Parliament and we will find mechanisms to make sure that doesn't happen", a senior party source said.