Fox launched the attack on UK companies, which he believes are not ready for the free trade deals he is planning to broker, while speaking at a drinks reception on Thursday night hosted by pro-Thatcher group Conservative Way Forward.
"This country is not the free-trading nation it once was. We have become too lazy, and too fat on our successes in previous generations," Fox said during his speech, the Times reported.
What is the point of us reshaping global trade, what is the point of us going out and looking for new markets for the United Kingdom, if we don't have the exporters to fill those markets?
We've got to change the culture in our country. People have got to stop thinking about exporting as an opportunity and start thinking about it as a duty - companies who could be contributing to our national prosperity but choose not to because it might be too difficult or too time-consuming or because they can't play golf on a Friday afternoon.
Fox, who was a prominent Leave campaigner in the run-up to the referendum, also blasted the Foreign and Commonwealth Office.
He said the department needed adopt a more mercantile stance instead of having a "cartographer's view of the world".
On the subject of import tariffs, he also indicated he will be unlikely to protect any sector of the economy with protective policies.
Read more: What now? The UK and the EU Single Market
"Protectionism has always ended in tears. We must be unreconstructed, unapologetic free traders," he added.
The newly-established Department for International Trade released and then quickly deleted a statement last month which said the UK could be left operating on World Trade Organisation rules after quitting the EU, until a fresh deal can be agreed.
Fox's comments about golf-playing executives sparked the ire of London-based leisure company Your Golf Travel.
"I've never heard a more out of touch comment in my life. Not only has golf secured the initial funding for my businesses but I've seen in network and create deals worth millions of pounds, four hours on the golf course can be worth a year on the phone," chief executive Ross Marshall said.
A spokesman for Fox said: "Dr Fox is committed to supporting the full range of businesses in the UK so that they can best take advantage of the opportunities that Brexit presents."