The UK is in "a new reality" following the EU referendum, David Cameron said.
The Prime Minister, who announced his resignation following last month's Leave vote, warned that there will be "other problems ahead" in addition to the recent fall in the value of sterling and the initial impact on the financial markets.
He made the comments at the Farnborough International Airshow in Hampshire, where he announced a long-term partnership with US plane maker Boeing which involves buying nine new P8 maritime patrol aircraft and expanding its research operations in the UK, leading to 2,000 new jobs.
Mr Cameron said: "Just over a fortnight ago the British people voted to leave the European Union.
"That went against what I recommended and I don't resile from what I said, from my warnings of a short-term shock, medium-term uncertainty and some long-term risks.
"Indeed we've already had a taste of the turbulence in global markets and in terms of the value of the pound and there will be other problems ahead.
"But I want to be clear - we will deal with them from a position of strength. With a growing economy, a greatly reduced deficit, with low inflation and more jobs and businesses than ever before in our country.
"Above all though, we must recognise we are in a new reality now. We must accept it, we must make it work.
"That's the way British business is responding to the referendum result."
Mr Cameron claimed the impact of the Brexit vote had created the biggest challenge to the British political system for 40 years.
He outlined what he believes are "the key things we need to get right" - Britain's relationship with Europe, its "underlying productivity challenges", the need to grow exports faster and encourage more inward investment.
"Above all, we need to think big and think radically about how to ensure the best possible outcome for the United Kingdom in these new circumstances," he told the audience.
"This amounts to the biggest challenge for the British political system that we have faced for around 40 years.
"It will require a massive national effort, not just for government departments, civil servants and ministers, but an effort that means working together with business and industries in a way we've never seen before."
The Prime Minister said the country needs to "make the most of the cards in front of us" and remain "very close" to the EU for trade, business and security.
He went on to "strongly advise" his successor that an "all-government effort" is required to tackle the UK's various challenges.
"When we are trying to break into new markets and sign new trade deals, we need all our economic, business and industrial might working together in the same direction - our business leaders, universities leaders and more," Mr Cameron said.
"When we are examining ways of driving up productivity, we need all the economic departments at the table - not just the Treasury, but education, infrastructure, regional planning, everyone.
"The threats we face don't neatly fit into one department's remit. I would say they are everyone's remit.
"Now it's a matter for the next prime minister what structures to set up, but I would strongly advise taking an approach like the one I have just set out."