Morgan, only 17, made her first competitive start for City during the clash and assisted Claire Emslie for the Blues' second goal.
As the club aim to develop more young talent, Cushing believes that the teenage defender fits the brief perfectly.
“One of the main areas of our strategy is to improve young players and particularly to improve young English players,” the City manager explained.
“That’s why we have the RTC (Regional Talent Clubs) and that’s why we have all of our teams - we want to put so much of our resource, our time and our experience into developing young players.
“Esme fits into that bracket and in pre-season this year there was an opportunity there and we brought her in.
“She trained really well and showed a lot of potential and I thought against Birmingham she was exceptional."
Although Sunday's match marked her first competitive start, the teenager featured in City's starting line-up during pre-season.
“Let’s not forget that her debut for us was a pre-season friendly against Lyon where she marked [Eugenie] Le Sommer, so she’s been put under a lot of pressure very early on!
“Against Birmingham I thought she showed that she has the potential to become a very, very good English player – but there’s a lot of hard work ahead.”
City take on Doncaster in the same competition on Wednesday evening away at Keepmoat stadium, kick-off at 7.30pm (GMT), before returning to the league on Sunday 10 December to play Chelsea.