Sturgeon was speaking as the Scottish government published Scotland's Place in Europe, a paper laying out what it said is "the first detailed plan dealing with the implications of Brexit published by any government to mitigate the economic, social, democratic and cultural risk since the referendum in June".
In the paper, the Scottish government laid out how it believes Scotland could remain within the single market, with free movement of goods, services and people, even if the UK leaves the EU. According to the paper, such a move would involve the devolution of more powers from Westminster to Scotland.
Areas that should be considered for devolution include import and expert control, immigration, competition, product standards and intellectual property, company law and insolvency, social security including the ability to set up reciprocal arrangement with other states, professional regulation, energy regulation, financial services, telecommunications, postal services and reserved acts of transport, according to the paper.
"There are already a range of differential arrangements in operation within the EU and in relation to the single market and the European customs union," Sturgeon said. "There is no reason 'flexible Brexit', [which has been] implied by the UK government in relation to different sectors of the economy, Northern Ireland and Gibraltar, cannot be applied to Scotland."
The paper represents a "significant compromise", Sturgeon said, in that the Scottish government believes full membership of the EU would be best for both Scotland and the UK.
Sturgeon also said that independence for Scotland would still be her preferred option and must "remain on the table".
"Without that option, Scotland would simply have to accept the inevitability of whatever decisions the UK government makes, no matter how damaging they are to Scotland's interests," she said. "However, independence is not the focus of the paper I am publishing today."
"The proposals are designed to respect Scotland's voice and protect our national interests, and I expect when the UK government considers these proposals, as the prime minister has committed to do, it demonstrates the same flexibility and willingness to compromise," Sturgeon said.
Sturgeon wrote in the Financial Times this week that she would prefer to see the whole of the UK remain in the EU. However, she said "the rhetoric emanating from a UK government that appears ever more in thrall to hardline Brexiters does not inspire great optimism".