Sturgeon now risks angering her own supporters if she attempts to block Brexit or continues calling for a fresh referendum on Scottish independence.
The revelation comes after the First Minister warned the Scottish Parliament could veto Britain’s decision to quit the bloc.
According to the Survation poll, 71 per cent of SNP supporters voted Remain – compared to 84 per cent of Lib Dems and 83 per cent of Labourites.
And 44.7 per cent of all voters said Scotland should not hold a second independence referendum, while 41.9 per cent were in favour.
Sturgeon said a new ballot on breaking up Britain is “very much on the table” because most Scots want to stay in the EU.
The poll shows 71 per cent of SNP supporters voted Remain last week
Scotland voted to stay as part of the UK – that should be that
He told the Daily Express: “That would be a slap in the face to the almost 40 per cent of Scots who voted to leave.
“We are a nation that has been united for 300 years. Scotland voted to stay as part of the UK and that should be that.”
Sturgeon has also insisted Scotland can stay part of the EU while keeping the Pound and retaining a border-free crossing with England.
She said: “We are in unchartered territory. England is our nearest neighbour and will always be, I hope, be our best friend.”
And she warned of “deeply damaging and painful consequences” of the Brexit vote and a “sense of bitter despair” north of the border.
The SNP leader said she would also tell her MSPs to refuse “legislative consent” if and when the Scottish Parliament was required to ratify the UK’s withdrawal from the bloc.
Speaking to the BBC she said: “If the Scottish Parliament was judging this on the basis of what’s right for Scotland then the option of saying look we’re not to vote for something that’s against Scotland’s interest, of course that’s got to be on the table.”