Reuters / Dylan Martinez
May met the leaders of Scotland, Wales, and Ireland - all of which have devolved governments - on Monday morning, and offered them a "direct line" to Brexit negotiations.
Sturgeon used the two-hour meeting to suggest a "flexible Brexit," according to the Herald Scotland, in which different parts of the UK could leave the EU on different terms.
62% of Scottish voters voted to remain in the EU, and Sturgeon - leader of the pro-independence Scottish National Party - has already announced plans for a second Scottish independence referendum. She has argued that Scotland has the right to opt for separation if it is not allowed to protect its interests "within the UK."
May ruled that out Sturgeon's "flexible" Brexit suggestion, according to the Herald, emphasising the need for a "single UK position," and warning other UK administrations not to act in a way that would "undermine the UK's position."
According to the Guardian, Sturgeon said after the meeting: "I'm not seeking to undermine anyone.... I don't know what the UK's negotiating position is, so there's nothing that I can see to undermine."
She added: "I can't undermine something that doesn't exist, and at the moment it doesn't seem to me like there is a UK negotiating strategy, which is one of the sources of great frustration."
Welsh First Minister Carwyn Jones echoed Sturgeon's frustration. He said: "There is still huge uncertainty about what success will look like from the UK government... That makes it difficult for the devolved administrations to positively influence the process."
He tweeted:
If UK Gov can't negotiate position with devolved nations little hope of negotiating a good #Brexit deal with 27 countries #JMC 3/3
- Carwyn Jones (@fmwales) October 23, 2016
The Scottish and Welsh governments favour remaining in the single market - a free trade agreement for countries within the EU - but May has suggested the UK will abandon it.
First Minister of Northern Ireland Arlene Foster, who campaigned to leave the union, has not yet made her position clear. Foster has not yet commented on the meeting.