The 30-year-old was penalised while taking a free kick in the 39th minute of the match.
With the ball just inside Man City’s half, Greenwood took around 25 seconds to find the pass.
But just as she went to take the kick, referee Emily Heaslip blew her whistle before giving the England Lioness a second yellow.
Greenwood, who stood still in disbelief, did not receive a warning prior to her dismissal.
And her team-mates were left furious as a result, with Laia Aleixandri, Jill Roord and Chloe Kelly also booked for dissent.
England legend Ian Wright took to social media to criticise the “embarrassing” officiating.
He tweeted: “Embarrassing. They keep telling us about laws of the game but where is common sense! Why would she be wasting time??? Kmt.”
Euro 2022 Golden Boot winner and Arsenal star Beth Mead agreed, adding: “Awful decision, never time wasting.”
THIS IS A DEVELOPING STORY…The Sun is your go to destination for the best football, boxing and MMA news, real-life stories, jaw-dropping pictures and must-see video.Like us on Facebook at https://www.facebook.com/TheSunFootball and follow us from our main Twitter account at @TheSunFootball.