Grealish has settled quickly into the Everton squad and has already proven to be a valuable addition, with his performance earning him the fans' admiration.
Moyes said that he had discussed with Grealish his potential and the importance of staying focused before he joined the team.
"I talked to him about it before he came," Moyes said. "I mentioned it, and I think sometimes you have to take players' flair, he's a bit of a maverick, he's been a great player, and if we could get the best out of him, it is what we needed at the time."
Moyes also acknowledged that Grealish's past experience at Aston Villa, where he was a fan favorite, might have influenced his decision to join Everton.
"The people at City said to me: 'You'll find he's a brilliant lad,'" Moyes said. "And at Aston Villa, all the supporters were asking me about Jack. I think it was because they see him on the way back to what he was for them and maybe enjoying his football as well."
Moyes expressed his confidence in Grealish's ability to build on his strong start to the season, saying that he believes the player has "another two or three levels to go."
"I genuinely believe he has more to come as well," Moyes said. "I want to keep pushing him a bit and challenging him to keep doing it. He's been assisting and we want him to score goals on the back of it as well, if we can."