The Supreme Court case was contested by campaign group For Women Scotland.
Its co-director Susan Smith claimed Sturgeon had been "disingenuous".
She said single-sex spaces were needed to provide women with "privacy, dignity, safety at time when they're vulnerable".
The campaigner told BBC Scotland News that it was "frankly wrong and quite disturbing" to claim that life would be "unliveable" for a section of society if they could not access those services.
Scottish Conservative deputy leader Rachael Hamilton said: "Nicola Sturgeon betrayed women and divided Scotland with her reckless gender self-ID policy, yet she still can't bring herself to apologise."
She added: "Nicola Sturgeon needs to hold her hands up and say sorry to the women of Scotland."
