Gareth Taylor‘s side started the brightest in front of a lively Joie Stadium crowd.
But, against the run of play, Chelsea took an early lead when Lauren James’ deflected effort snuck in at Khiara Keating‘s near post.
City continued to press for a route back into the game, with Khadija ‘Bunny’ Shaw twice forcing Hannah Hampton into action before the Chelsea stopper pulled off a brilliant save to deny Lauren Hemp from close-range.
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The hosts were then incensed that calls for a penalty after Alex Greenwood went down in the box in added time fell on deaf ears.
It was a frustrating end to a game which City will feel they did enough to force extra time at the very least.
But with an important FA Cup quarter-final against Spurs on Sunday, the players have an opportunity to regroup and get back to winning ways.
Watch the extended highlights in the video player above.
