Gareth Taylor’s side suffered a 4-0 reverse at the Academy Stadium, falling to Emma Hayes’ side at home for the first time in the league.
Although Greenwood admits the setback was a bitter pill to swallow, she has implored the City faithful, who turned out in numbers for Women’s Football Weekend, to stand by the team and stick together during this tough period.
“The result is disappointing,” she said. “Some of our play was outstanding but you have to put the ball in the back of the net and eliminate the mistakes.
"Stick with us. The turn out today was fantastic.
"Keep believing in us. It will come to light at some point."
Though the result saw City slip to ninth in the table – 11 points behind second-placed Chelsea – Greenwood refused to throw in the towel, adding her side will stay true to the Club’s philosophy and principles as we bid to turn the season around.
"No, honestly no. I'd be a fool to say that,” she replied, when asked whether City’s title challenge was over.
“What’s the point in playing the game if that’s how you feel?
"We've got to keep putting performances in and results will come.
"We'll always play this style - it's the City way to play.
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"There'll always be mistakes - that's part of football - but we need to stop making them early on in the game and give ourselves the best chance of staying in the game for long periods.
“The difference is that they put the ball in the back of the net and we didn’t.
“We’ll go away and work on that and go again.”