Jo Coburn quizzed the Labour politician on BBC Two's Daily Politics on Monday after he released his plans with Plaid Cymru leader Leanne Wood.
She said his plan will mean "we won't have left [the EU]" after accusing him of wanting to "sneak back in" the European Union.
The joint paper suggests the UK could become a member of the European Free Trade Association (EFTA) and European Economic Area (EEA) in order to achieve “full and unfettered access to the Single Market”.
Mr Jones said: "What's important is we don't re-fight the referendum – that's done. We still talk about Remainers and Leavers – it's finished, forget about that.
"It's a question now of how. How do we leave in the most beneficial way possible to Wales and the other nations."
BBC TWO/DAILY POLITICS
Jo Coburn and Carwyn Jones clashed on Daily Politics
It sounds like you're accepting leaving and then you want to sneak back in
Jo Coburn
Coburn fired back and said: "But it sounds like you're accepting leaving and then you want to sneak back in."
The First Minister insisted it was not a question of leaving, but "how" the UK leaves the EU.
"Lots of people, Arron Banks, Daniel Hannan, people who are very Eurosceptic said that, for example, the Norwegian model was one that we could look at," said Mr Jones.
"And now they're saying 'no, we don't look at that'. Well, in fact, the Norwegian model works pretty well – they have access to the single market, they're not in the EU."
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The host responded by saying Norway had to sign up to the European Union's fundamental four freedoms – free movement of goods, capital, services and people – as a result of being in the single market.
"The four freedoms include, as you know, freedom of movement of people, which the Government has said they felt that was the message in the vote," she said.
"If you take the Norwegian model, you also have to sign up to the European Court of Justice or certainly an equivalent in terms of a court who will oversee any disputes – so we won't have left."
But Mr Jones said it would be the same with regards to a free trade deal in terms of being subject to an independent body in order to resolve disputes.
BBC TWO/DAILY POLITICS
The Welsh First Minister is in favour of single market membership
GETTY
Norway's trading arrangements with the EU have been cited as a possible example for Britain to follo
He then explained how Norway had signed up to free movement but "not in the way the UK has done".
He said: "What Norway has done is said 'okay you've got freedom of movement to come here if you've got a job'.
"On top of that, if you lose that job, you've got three months to find another one or you have to leave.
"Now I think that's actually a rational, common sense way of dealing with people's concerns but in a way that makes it easy for us to recruit the doctors and nurses that we need."
Neil Hamilton, Ukip’s leader in Wales, described the Welsh Government’s paper as nothing but a “collection of soundbites”.
He told Express.co.uk: “This is a kind of primal scream from those who lost the referendum and they’re trying by the back door to keep us in the EU.”
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