The result has seriously dented their hopes of qualifying for the Women’s Champions League, extending their winless domestic run.
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They remain fourth in the WSL, one point behind Arsenal despite playing more games.
"I hear it, I feel it. I'm at the head of the football club. I'm accountable, right? I'm there for people to give their opinion,” Skinner told BBC.
“I work tirelessly hard to push this football club. Everyone's entitled to their opinion. I will never deny that but there's no-one more disappointed than me today for not taking three points."