McKenna’s own goal helped the hosts get the upper hand but Lewes had a second-half penalty saved by Shae Yanez.
Josie Longhurst, Lewes midfielder, said: “It’s disappointing that we ended up with the loss. They scored early and we were continuing the game. It’s disappointing not to bring the game back because I think that we were all over them.
“We kept energy all the way. Towards the end we had a lot of chances. It’s just to put them aside. I think we had to be focused in those moments, make these races and connect us with the ball.
“We got past them at times. One and two touches around them. If we had scored our chances, we definitely deserved the win. It’s hard to go on a game. It was that first goal, and we didn’t could not score our ultimate chances.
“I think we can take our energy and our performances. I think we played very well, we connected our passes, one, two touches, and we stayed together.
“I think we deserved more, and we’ll take that into account in our next game and make a switch against Coventry.”
The Lionesses took the lead after five minutes when Karin Muya’s cross in a promising attacking position bounced off the hapless McKenna before finding the back of the net.
Lewes felt they should have had their own penalty in the 12th minute when London City goalkeeper Yanez knocked Freya Ayisi down in the box but it was dismissed.
Ten minutes into the second half, Lewes was awarded a penalty for a foul in the box. But former Lionesses player Ayisi was prevented from equalizing by Yanez’s superb save. The American dove to her right to tip the ball at the foot of the post.
The hosts should have doubled their advantage through Amy Rodgers. First, his ferocious 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 which also didn’t find the back of the net.
Lewes saw a late chance hit the post as the visitors failed to get anything out of the game. The Lionesses then travel to second-placed Bristol City in ten days, while Lewes face the trip to Coventry United on the same day for their penultimate league game.
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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. Subs: Paula Howells for Longhurst 70, Zoe Cross for Hazard 70, Ellie Noble for Dalton 86, Georgia Timms for Ayisi 86. Unused substitutes: Laura Hartley, Shanell Salgado, Nicola Cousins, Heidi Logan, Lea Cordier
Referee: Sophie Dennington