The 36-year-old actress - who has three-year-old Jonathan and is expecting her second child with husband Adam Shulman - believes everyone has a "responsibility" to stay away from disposable items of convenience and should think carefully about throwing things away.
She said: "[I have] cared about the environment for a really long time. When I had my son I started to think about consuming things in a different way.
"I think I was like everyone in that I would just use things and then not think about what happened when I threw it out.
"I think we all have a responsibility to not just mindlessly follow the path of convenience. And I know that is an incredibly privileged thing to say. That not everyone has a choice, but everyone can do something."
The 'Modern Love' actress also heaped praise on 16-year-old activist Greta Thunberg and argued the teenager's critics have displayed "textbook misogyny".
She told the Evening Standard newspaper: "If you think about the way she is being criticised, it is textbook misogyny, textbook patronising, it is all these things.
"I think one of the best things to focus on about her is she speaks from a place of passion and emotion. She is speaking science to power.
"I admire her and I am glad to see I am not the only one."
Meanwhile, Anne praised the portrayal of mental health issues in her new Amazon Prime Video series 'Modern Love'.
She said: "I can't remember another character I'd come across as an actor or as a viewer [who was a] bipolar woman trying to find love. The inclusion of that story seemed very modern to me. And that can't be a bad thing."