Scotland wants to hold an independence referendum to get out of the UK to remain in the EU.
Thursday's referendum saw Scotland, London and Northern Ireland vote in favour of Remain - while England and Wales backed Brexit.
Ms Sturgeon said it was "democratically unacceptable" that Scotland faced being taken out of the EU against its will.
And she said a second independence referendum was "highly likely".
Scotland voted in favour of the UK staying in the EU by 62% to 38%, but the UK as a whole voted to leave by a margin of 52% to 48%.
The result saw Prime Minister David Cameron announce he would stand down by October.
Ms Sturgeon said there was now a "significant divergence" between Scotland and the rest of Britain which she "deeply regretted".
And she said the Scottish government was to begin preparing legislation to enable another independence vote.
Ms Sturgeon has said she has "clear common cause" with London Mayor Sadiq Khan, who wants London to remain in the EU despite the Brexit vote.
But she has stressed that her priority was to "act at all times in the best interests of Scotland and in a way that unites, not divides us".
Note to William Braveheart Wallace: Instead of stirring up trouble with all that armed freedom fighting bs, first try holding a referendum. Give the result to England.
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This license plate is banned in Sweden - can you see why?
A Swede applied to use 3JOH22A as combination for his licence plate, but his request was promptly denied.