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Liverpool manager Matt Beard said they were "let down by officials" after the decision to award Everton a penalty in the Merseyside derby.
Everton won 1-0 at Goodison Park, picking up their first win in the Women's Super League this season, thanks to Katja Snoeijs' spot-kick shortly before half-time.
Referee Abigail Byrne awarded a penalty when Fuka Nagano clipped Honoka Hayashi but replays show the foul appears to be outside the area.
"It wasn't a penalty. That's it. It changes the complete complexity of the game," said Beard in his post-match media conference.
"You have the referee, the fourth official, the linesman and the assistant referee all with unblocked views. Even I saw the contact was about a yard outside the box.
"I just give up with it to be honest with you because it happens every week - not just with us. It's cost us the game today, 100%."
Beard's frustrations grew throughout the match as Liverpool had appeals for two penalties for contact on Olivia Smith and Ceri Holland waved away late on.
It leaves them with just two victories from their opening eight matches, while Everton climbed off the bottom of the table.
"I just feel we've been let down by the officials," added Beard. "I feel we should have had two penalties and we've had one given against us that wasn't a penalty.
"Ultimately those decisions have cost us either a point or three points today."
Beard believes referee Byrne will "have to own up to her mistake" because it is there for people to see on TV replays.
Asked if Liverpool will make a complaint to refereeing body PGMOL, Beard said there was "no point".
BBC Sport has contacted PGMOL for a comment.
Liverpool did have chances to equalise in the second half with Marie Hobinger, Gemma Bonner and Nagano all coming close but Everton goalkeeper Courtney Brosnan was in fine form.
Bonner, who forced a smart save from Brosnan late on, said the decision from Byrne to award a penalty in the first half was "frustrating" for the players.
"It's there for everyone to see. As players it is frustrating. It ultimately decided the game," Bonner added.
"There are things we can control ourselves but as players all we ask for is honest decisions.
"Everyone is gutted. We had the decision go against us but there are a lot of things we can do better."
The decision raises the question once again of whether video assistant referee should be introduced in the women's game.
Everton manager Brian Sorensen said he would welcome the use of 'VAR Lite' - a system that has been trialled in youth football international tournaments.
"They can just press on a laptop then go five seconds back. For me, I don’t know why it’s not here now," he added.
"It will take so many things away because [the referees] just need that little bit of support. That’s what we do as coaches. We go back and see ‘oh, that’s clear’.
"If it’s something you have to look at from seven angles then for the joy of the game, maybe not. But if it’s clear, it will take a lot of disputes away."
Sources have told BBC Sport that Women's Professional Leagues Limited (WPLL) - the company that oversees the WSL - is working with clubs to ensure that venues can provide VAR for when the board considers its introduction.
The biggest factor for VAR not existing currently is that not all venues in the WSL have the capacity to implement the technology. And there is uncertainty over whether clubs will be able to afford it.
"The money is not there for VAR. I don't know what the answer is to be honest with you. I think every manager feels the same every week," said Beard.
"[Referees] come out and tell us they will implement the rules, then they don't. I don't know whether they don't like me personally as well and whether that has an effect on my team - it could do.
"I've been booked for things when I've seen other managers get away with it. I don't know what the answer is any more, I really don't know."