The First Minister insisted Mrs May's flagship Withdrawal Bill is not acceptable despite "constructive and cordial" talks.
She was speaking after her first one-to-one discussions with the Prime Minister since the Brexit process was formally launched in March.
The Nationalists have repeatedly threaten to hinder the legislation by withholding consent amid claims of a Westminster "power grab" over areas such as fishing and farming.
UK ministers argue that some UK-wide frameworks will be required in devolved areas to protect the single market by replicating European Commission rules.
. / EPA
‘Not acceptable!’ Sturgeon renews Brexit threat after crunch talks with Theresa May
While we didn’t reach agreement, we developed a better understanding of each other’s positions
They have pledged that the Scottish Parliament's powers will not be diminished as a consequence of Brexit but have been unwilling to publish specifics.
During their 45 minute summit at Number 10 also discussed the sex pest scandal and engineering firm Burntisland Fabrications Limited (BiFab) which is on the brink of collapse.
Ms Sturgeon described the talks as "constructive and cordial" but said she had "not yet" heard anything from Mrs May that made her think she could now recommend that Holyrood gives its consent to the Bill.
She said: "While we didn’t reach agreement, we developed a better understanding of each other’s positions."
Ms Sturgeon insisted Mrs May's Withdrawal Bill is not acceptable
Ms Sturgeon said she hoped to see progress in "the weeks to come" but added: "On the Withdrawal Bill, there’s a long way still to go, and I'm very clear as I have been all along that bill has to change."
The meeting came after Nationalist MP Tommy Sheppard threatened another independence referendum if the UK Government was to "overrule" Scottish "representations" on Brexit.
Tories urged Ms Sturgeon to lift the threat.
PM and Sturgeon feign smiles as they go to battle over referendum
Wed, April 5, 2017
British Prime Minister Theresa May met Scottish First Minister Nicola Sturgeon in Glasgow, following the announcement that Scotland is to hold a second Independence Referendum
SWNS.com 1 of 10
British Prime Minister Theresa May meets Scottish First Minister Nicola Sturgeon in Glasgow, following the announcement that Scotland is to hold a second Independence Referendum
Ms Sturgeon said Mr Sheppard was "articulating" her government's "longstanding position" and reiterated that she will not consider the issue until "the terms of Brexit are clear."
A Number 10 spokesman said the Prime Minister had emphasised to Ms Sturgeon that "as powers are repatriated from Brussels back to Britain there will be a significant increase in the decision-making powers for the Scottish government and other devolved administrations".
The spokesman added: "The Prime Minister encouraged the Scottish Government to continue to work with counterparts to secure the best outcome for the people of Scotland and the whole of the UK."
- ‘Standards are worse!’ Sturgeon urged to abandon tax hike plans
- Nicola Sturgeon is ’SEEKING CLARITY’ on Brexit issues with Theresa May
- SNP threatens independence referendum if Sturgeon ignored on Brexit