The leadership contender said he would not be aiming to pull the UK out of the bloc without a deal, though acknowledged that such a scenario could not be ruled out, Efe news reported.
Johnson, the former Mayor of London who went on to serve as Foreign Secretary in May's Cabinet and subsequently resigned from that role, said the population felt "disillusion or even despair" when it came to the government's ability to get the UK out of Europe.
He said that the public would be relieved after Brexit as it would allow the country to focus on other pressing issues.
Johnson said the government was stuck at a crossroads, warning there was a risk that the population would lose confidence in politicians if the situation carried on as it was.
For Johnson, a new setback for Brexit would be the opposition Labour Party of Jeremy Corbyn getting into government.
The former London Mayor drew on his experience in that post, saying he had got the capital through riots, strikes as well as overseeing the Olympics in 2012.
He now seeks to replicate what he did for London across the whole country, he said.
According to Johnson, the country needs to be united and it needs better infrastructure, including faster broadband and more metro networks.
The Conservative Party finds itself in the throes of a leadership contest after May failed to get her deal with the EU passed in Parliament on three occasions.
She stepped down from the top office on June 7, maintaining the role on a caretaker basis until a replacement gets chosen in July.
There are 10 Tory lawmakers vying to become the next leader of the party and the UK's next Prime Minister during a turbulent time for the country.