
The Blues midfielder had burst through the Liverpool backline and looked set to collect a ball over the top to present Dewsbury-Hallwith a glorious chance to give his side the lead.
Instead, he fell to the floor only for referee Chris Kavanagh to wave away the appeals of those in Royal Blue - leaving Moyes furious on the touchline.
Asked whether he believed Everton should have been given a penalty, the manager, who in the build-up to the match complained over his belief the Reds tend to get more favourable decisions, said: “I do, yeah. Why would he go down if he's not?
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“You might say it could go down as a soft contact or whatever but, well, if he touches him at all, why would he not [take the chance to shoot], he's in on goal to shoot and finish, why would he not take the opportunity to do that?”
Aside from that call, Moyes believed his side deserved the point that was taken from them by Virgil van Dijk’s header in the tenth minute of stoppage time.
The Blues boss said: “We didn't deserve the outcome we got, football's cruel sometimes and we have to bounce back and go again when adversity goes against you.”
Everton had done just that when Beto equalised in the second half to cancel out Mohamed Salah’s opener - a goal that had come against the run of play after an excellent start failed to yield a goal for the hosts.
Moyes, who conceded he was “worried” about the condition of Jarrad Branthwaite after the centre-back was stretchered off late on, said: “I thought we were the better team for the first 25-30 minutes, I don't know how long, but I thought Liverpool were better in the period just before half-time.
“They started the second half a little bit better, but when we got back in with a goal, I thought that we were the better team.
“If anybody was going to score, it was certainly going to be us.
“I don't think the injuries we had helped us in some ways, you know, just to change it, but hey, I've got no problem, the players did a great job today, did a good job in competing against a really strong team.
“We showed that we're not too far away.”