Lewes: We didn't deserve to lose to London Lionesses
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McKenna's own goal helped the hosts edge the contest, but Lewes did have a second-half penalty saved by Shae Yanez.
Josie Longhurst, Lewes midfielder, said: "It's disappointing we ended up with the loss. They scored early on, and we were chasing the game. It's disappointing not to bring the game back because I think we were all over them.
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Hide Ad"We kept energy the whole way through. Towards the end, we had lots of chances. It's just putting them away. I think we needed to be focused in those moments, get those runs in and connect with the ball.
"We outplayed them at times. One and two-touch passing around them. If we'd scored our chances, we definitely deserved the win. It's hard to chase a game. It was that early goal, and we couldn't score our final chances.
"I think we can take our energy and performance. I think we played really well, we connected our passes, one, two touches, and we stuck together.
"I think we deserved more, and we'll take that into our next game and put in a shift against Coventry."
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Hide AdThe Lionesses took the lead after five minutes when Karin Muya's cross in a promising attacking position rebounded off the unfortunate McKenna before finding the back of the net.
Lewes felt they should have had a penalty of their own in the 12th minute when London City goalkeeper Yanez brought down Freya Ayisi in the box, but it was waved away.
Ten minutes into the second half, Lewes did get a penalty for a foul in the box. But former Lionesses player Ayisi was prevented from equalising by Yanez's great save. The American dived low to her right to tip the ball onto the foot of the post.
The hosts should have doubled their advantage through Amy Rodgers. First, her fierce shot from the edge of the box with 15 minutes to play went just wide. And then she had a header on target six minutes later that also did not find the back of the net.
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Hide AdLewes saw a late chance hit the post as the visitors failed to take something out of the game. Lionesses next visit second-placed Bristol City in ten days' time, while Lewes face the trip to Coventry United on the same day for their penultimate league fixture.
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Lewes (3-5-2): Tatiana Saunders, Ellie Mason, Amelia Hazard, Ellie Hack, Lucy Ashworth-Clifford, Freda Ayisi, Rebecca McKenna, Sophie O'Rourke, Josie Longhurst, Izzy Dalton, Lucy Porter. Substitutes: Paula Howells for Longhurst 70, Zoe Cross for Hazard 70, Ellie Noble for Dalton 86, Georgia Timms for Ayisi 86. Substitutes not used: Laura Hartley, Shanell Salgado, Nicola Cousins, Heidi Logan, Lea Cordier
Referee: Sophie Dennington