The Toffees had recovered from conceding a goal to Theo Walcott after just 52 seconds with Marouane Fellaini scoring his seventh Barclays Premier League goal of the season.
And when Steven Pienaar went down under a challenge from former Everton midfielder Mikel Arteta in the second half Moyes was convinced Jones got it wrong in awarding only a corner.
"It was a penalty. We played Arsenal today [Wednesday], who are a really good team, but we also had very few decisions go for us," he said.
"Sometimes referee's decisions change the games: in some games something might go in your favour but we were never going to get that tonight [Wednesday].
"We got nothing whatsoever and anything we were going to get we had to earn on our own because we were not going to get a jot.
"There was an incident when the ball got chipped into the box later on and he gave a push on Fellaini.
"I've had a chance to see it and it was never anything like it. I found that one as mystifying as any really.
"We found it a difficult night from that point if view but the players played really well throughout."
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The difficult night continued with Leighton Baines, Everton's stand-out player of the last two seasons, sustaining a hamstring injury which makes him a major doubt for the weekend trip to Manchester City.
"He felt it in the game and played on in the last 10 or 15 minutes," added the Scot.
"I felt we out in a lot of energy tonight [Wednesday] but it might take its toll.
"We've got Gibbo (Darron Gibson) and Hibbo (Tony Hibbert) back and that has eased it a little bit but I am worried about Nikica Jelavic (ill) who has not trained since Saturday and yesterday [Tuesday] I was not playing him."