The Gunners won 1-0 thanks to a successful penalty from Viktor Gyokeres in the first-half.
On Arsenal's winner, Moyes said: "Yes, and a really poor penalty from our point of view. If you're going to lose to Arsenal, you hope you might lose to Arsenal by a goal, which they're more than capable of scoring.
"So it was a poor decision by Jake (O'Brien), he shouldn't have raised his arms above his head at the action, but look, he feels he gets slightly pushed from behind and that caused his arms to fly up."
On Everton being denied a penalty involving Thierno Barry, Moyes was adamant.
"I think we could have done. I think on another day somebody might have given a penalty. I think (William) Saliba kicks the back of Thierno's Achilles, it looks like, and it's not as if he's sort of pulled his foot away, he's kicked through.
"I just think it looked like a bit of an action where there wasn't much happening, and Thierno's got in front of him and he's kicked. I don't know if the referee was expecting it or VAR, but it didn't go our way. We've not been getting many decisions here, that's for sure."
One positive from the night was Tim Iroegbunam's performance and Moyes added: "I thought Tim played well. I think Tim has played well at different times for us.
"We want him to look to play forward a bit more and be a bit more positive, but his retention of the ball and his work was very good and he's done a good job against Declan (Rice) tonight."