The politician, who is standing for reelection in Moray – a Brexit stronghold in Scotland – insisted Remainers and Brexiteers alike feared leaving the bloc.
He claimed Leave voters were sold a different version of Brexit at the time of the EU referendum, which saw 38 per cent of Scots wanting to break from the EU.
Mr Robertson told Channel 4 News: “People who voted both Leave and Remain are very concerned about the hard Tory Brexit that’s being pursued by Theresa May because that’s not what they were promised.
“We have food producers in Moray that are known right around the world. If we want those companies and those businesses to succeed, to be able to export, we need access to the single European market.
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Angus Robertson said Brexit backers in Scotland did not want a "hard" Brexit
People who voted both Leave and Remain are very concerned about the hard Tory Brexit that’s being pursued by Theresa May
“The SNP is fighting for that, the Tories have already sold their pass on that.”
But the SNP has used the Brexit vote to call for a second independence referendum in order to stop Scotland from exiting the bloc along with the rest of the UK.
Tory candidate Douglas Ross, who is going up against Mr Robertson in Moray, which saw a 49.9 per cent Leave vote, said the SNP was “obsessed” with independence.
He said: “There’s only one issue coming up in Moray and indeed many parts of Scotland and that’s the SNP’s decisive plans for a second independence referendum and people clearly don’t want it.
Nicola Sturgeon's comical moments on the campaign trail Mon, May 22, 2017 PA 1 of 13
SNP leader Nicola Sturgeon stops for an ice cream after making an election campaign visit to Scottish Gas HQ in Granton, Edinburgh
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“It’s absolutely the main issue and it’s not just Conservatives, it’s people from the Labour Party, Liberal Democrats, people who aren’t affiliated to any political party and indeed SNP supporters –people who voted Yes two and a half years ago.
“[They] are fed up of Nicola Sturgeon’s obsession with a second independence referendum at the expense of many other issues that people think we should be concentrating on.”
According to a new Ipsos MORI poll, the First Minister popularity has plunged over her fight for independence.
The First Minister's personal approval ratings collapsed from +14 to -4 since September last year, a period which included her demands for another ballot on breaking up Britain.