Vicky Jepson's side gave a good account of themselves in a goalless opening 45 minutes in the Women's Super League encounter, but City's quality in the final third ultimately saw them get the three points.
Before kick-off, both teams observed a minute's silence as a mark of respect following the tragedy that unfolded at Leicester City's King Power Stadium last Saturday and also ahead of Remembrance Day next weekend.
The Reds went into the game without the influence of attacker Jess Clarke but goalkeeper Anke Presuss was available to start after returning from injury.
The stopper showed her quality on eight minutes when she made a brilliant save to keep out a Jennifer Beattie header following a corner.