The win was City’s first of the WSL season with Bunny Shaw opening her league account at the Joie Stadium.
Greenwood was keen to highlight the improvement of how the Blues played off the ball since the game against Arsenal last Sunday.
City started their WSL campaign with a 2-2 draw at the Emirates, but Greenwood was pleased we could hold on for the win this time.
Speaking to the BBC after the game, she said: “We got the job done. Sometimes in this league you have to win ugly. I thought off the ball today we were better.
“Against Arsenal we struggled with that at times, but we have worked really hard on that, and I thought we saw an improvement in that today.
“This league is getting tougher and tougher ever year, and we saw that with Brighton today, it was a tough game. We take the win and the clean sheet all day. “
City will be hoping this carries on to the next game where City face West Ham United Women at The Joie Stadium.
A UEFA Champions League game against Barcelona follows and Greenwood hopes City can build on the Brighton victory going into those games.
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“When we get it right we can cause teams problems. Again it’s work in progress,” she added.
“At times stepping out with the ball we could have been a bit tidier today but defensively I thought we were good with the ball.
“They had a lot of the ball, but it didn’t feel like they caused us a massive amount of problems.”
