The SNP leader insisted it would be wrong to "keep quiet" about the feared damage to the economy and society from leaving the EU.
The First Minister has also been critical of Theresa May's approach to negotiations, but admitted today that the Tory leader's flagship speech on Friday was more "realistic."
It was put to Ms Sturgeon today that the EU is likely to reach a favourable deal for the UK's exit if they see a "divided Britain."
"Aren't you in a a sense doing Scotland and Britain down by undermining the Prime Minister?" Ms Sturgeon was asked on ITV's Peston show.
"I think, and everything that I heard from the Prime Minister on Friday seemed to underline this point, that if we're leaving the EU, which I deeply regret, then the least worst option is to stay within the single market and the Customs Union."
The First Minister said Mrs May's speech on Friday made it clear that the UK would be "worse off" after Brexit.
"Why would any First Minister of Scotland or First Mniister of Wales or anybody else who is interested in the long-term prosperity of the country just accept that?
"I don't believe even those who voted to leave the EU, and I respect their opinion, were voting to make themselves or anyone else worse off. But that's going to be the outcome of this.
"I think it makes it all the more important that people like me continue to argue for what I would consider to be a much more common sense approach."