But he said the threat of no deal was a "vital" negotiation tool and the United Kingdom "must do better" than the current deal.
His warning came after the Commons narrowly voted on Wednesday to reject a Labour motion - backed by other opposition parties - which would have enabled MPs to take control of the business of the House on June 25.
The leadership hopeful said delivering Brexit alone was not enough to secure a majority at the next general election, and set out his plan to recruit an additional 20,000 police officers and invest in education.
"We can't risk going with someone who feels like the short-term, comfort zone choice".
The Brexit deal has been delayed twice, during May's tenure the most recent deadline being October 31.
Scottish Conservative leader Ruth Davidson, who introduced him at Wednesday's event, said Mr Javid would give voters a "greater reason to feel pride" in the UK.
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The EU has insisted repeatedly that it will not renegotiate the terms of the divorce, while parliament has previously voted against leaving without an accord.
He said: "For three times when the opportunity presented itself to me I have not voted for a deal, the last time in March I followed my party line that I would not support the deal that was put in front of me - and I made a mistake".
The contest so far has been dominated by revelations of past drug-taking by candidates and bickering over the best way to resolve the Brexit impasse.
He has kept a low profile in the race to succeed Theresa May so far, his only significant intervention being a pledge - immediately criticised by his rivals - to cut income tax bills for people earning more than £50,000 a year.
Johnson's supporters believe he is the only leader who can win against the twin threats of leftist Labour leader Jeremy Corbyn and eurosceptic Nigel Farage. He added, "Delay means defeat, delay means ruin". She stepped down as Conservative leader last week, setting the stage for a weeks-long process to select a new Tory leader and prime minister.
Johnson, a leading figure in the 2016 referendum vote to leave, has said he will deliver on the result with or without a deal with Brussels.
Johnson kicked off his official campaign on Wednesday with a pledge to lead Britain out of the European Union on October 31 and a warning to his divided Conservative Party that "delay means defeat". "Labour stands ready to use whatever mechanism it can to protect jobs, the economy and communities from the disastrous consequences of a no deal Brexit", Starmer said in a statement.