The First Minister’s response came after Theresa May restated plans to remove Britain from both the European single market and the customs union.
The Prime Minister used a key speech in London to set out her vision of a future relationship with the European Union, which she said Britons could unite behind to create a “stronger and more cohesive nation”.
The Conservative leader repeated her “red lines” that the UK will leave the single market and customs union and the jurisdiction of the European Court of Justice.
She also went into greater detail on the customs arrangements Britain wants to avoid a hard border with Ireland.
One of the five tests the government will apply to Brexit is that any deal must strengthen “our union of nations and our union of people”.
She insisted she was “confident” a deal was “achievable”, with Mrs May telling Brussels: “Let’s get on with it.”
However, the Scottish First Minister branded the government’s “determination” to pursue a hard Brexit – that would remove the UK from the single market and the customs union – as “bizarre”.
Ms Sturgeon said: “She accepted that access to the single market – the world’s biggest marketplace and one around eight times bigger than the UK’s alone – would be reduced, yet said she would leave the single market and customs union anyway, even though her own government’s analysis shows this will cost jobs and cut living standards.”
The SNP leader added: “The EU has already rejected the Prime Minister’s wish-list approach, but even if she can somehow persuade them to adopt everything in this speech, we will still get a worse deal than we have today.
“Scotland voted overwhelmingly to remain in the EU and it is time for the UK Government to take seriously the proposals we have made to keep Scotland and the whole of the UK in the single market and customs union.
“It is regrettable that the UK Government has consistently failed to engage properly with the Scottish and other devolved governments, and it is essential we now have a meaningful role in the forthcoming negotiations.”
Scottish Labour leader Richard Leonard said: “The idea that we can trust the Tories to strengthen the Union of nations that make up the United Kingdom is simply unbelievable.
“Theresa May’s shambolic handling of Brexit has sent the United Kingdom hurtling towards a constitutional crisis with damaging consequences in Scotland, Wales and Northern Ireland.
“From failing to protect the devolution settlement to the disgraceful mishandling of Northern Ireland’s future, this is a Prime Minister who has endangered the Union by failing to stand up to her own right-wing backbenchers.”
Scottish Liberal Democrat leader Willie Rennie said the speech had “only strengthened the case for giving the British people a vote on the final deal, with an option to stay in the EU”.
Scottish Conservative leader Ruth Davidson insisted the PM had “set out a pragmatic, realistic plan which gives us the basis for the next round of negotiations”.
While Mrs May accepted “not everyone will get what they want out of those talks”, the Scottish Tory said the Prime Minister had “made clear that she wants to construct a deal that delivers as much common ground as possible, respecting the result while also maintaining close ties with our friends and allies on the continent”.
Ms Davidson also said she welcomed the “commitment to protect the integrity of our own Union as we leave the EU”.