Arteta has been below par for much of the season but his return to form at Goodison Park on Saturday coincided with a 2-0 victory over Sunderland and prompted Moyes to compare him to the 2010 FIFA Ballon d'Or runner-up.
Moyes fought hard to keep highly-rated Arteta at Everton during the summer and hopes that the Spaniard's recent performances are a sign that he will soon be back to his best.
"I thought he did well [against Sunderland]," Moyes told the Liverpool Echo. "He made the second goal with a bit more like what we've seen from him. I thought he was more in the thick of things, competitive as well, winning a few things in the middle of midfield.
"People said they think he's played safe. I don't. I think he's kept the ball for us. People talk about Iniesta with 95 passes and something like 94 were accurate. You have to keep the ball and Mikel can keep the ball for us. He's very comfortable on it."
Arteta won rave reviews last season and Moyes thinks the 28-year-old may have struggled this term because he has tried to take too much responsibility as Everton's playmaker.
Moyes said: "Maybe he felt he's had to be the one who makes us play, get on it, get the ball for us, make us pass, because we've tried to improve our play. And maybe in the end he's taken too much responsibility on.
"In turn his form has dipped. We've probably said to him recently, 'Go on - just get on with the game and in time your form will come back.' And as I said, there are signs that it is.
"We've asked him to try and get forward, get in the box and get on the edge and have a shot, and get into positions where he feels he can score a goal and he's looked more like himself."