And she argued that the UK-wide result of the EU referendum was not a mandate for a hard Brexit.
Ms Sturgeon was addressing the Institute of Directors annual conference at the Royal Albert Hall in London.
The SNP leader told the conference that continued membership of the European single market was the “obvious consensus position” among Leave and Remain voters in the EU referendum – and that the UK-wide result was not a mandate for a hard Brexit.
But she acknowledged that certain aspects of single market membership, such as freedom of movement, “will not satisfy everyone”.
She also argued that inequality was a key reason behind the EU referendum result, and that the UK government “can no longer ignore the social and economic cost” of austerity.
She said: “There are many, many causes of the vote to leave the EU. For many people, they will have included entirely reasonable doubts and reservations about the EU. It is, after all, an imperfect organisation.
“But in part, Brexit was a product of a sense of disenfranchisement and disillusionment. It was borne of inequality, of feelings of powerlessness – of austerity budgets which hurt the public services and social safety nets that so many people depend on.
“And so one consequence of the referendum must be a new effort – which needs to be given real substance in the UK government’s autumn statement – to ensure that the benefits of growth, of globalisation, are more fairly distributed.”
Ms Sturgeon said she was “very proud of the fact that Scotland voted so strongly to remain in the European Union”, but that should could not ignore the fact that a million Scottish voters wanted to leave.
She added: “They did not think that the European Union benefited them – they did not see advantages from free trade and free movement.”
It was Ms Sturgeon’s first major speech to a UK audience since the referendum in June, although she has made numerous statements on the issue at Holyrood.
Ms Sturgeon has told MSPs she is “profoundly concerned” about the implications of the UK leaving the EU, with the early signs “not encouraging”.
She has also argued that the “least worst option” of remaining in the single market should be a key objective, hitting out at the “cloak of secrecy” over the UK’s current negotiating position.
Mrs May meanwhile has said the UK could get a better deal from foreign trade after leaving the EU.
In a column in Holyrood magazine which she later posted in full on Facebook, the prime minister said Brexit represented an “exciting chance to forge a new role in the world”.
She said the UK would “make a success” of Brexit, saying: “There should be no doubt: we will get a deal that works for us all.”
Mrs May said: “As we strike that deal, we have an exciting chance to forge a new role in the world. Scotland’s status will not be diminished by that; it will be enhanced.
“We will go out into the world with the aim of being a leader in global free trade, one that makes the most of our advantages, from the financial expertise of Edinburgh to the shipbuilding prowess of the Clyde and the globally renowned food and drink produce of Scotland’s countryside.”