“I’m really pleased for him. You’d have to say it’s a big privilege to be given that accolade and I’m pleased for him because everybody knows he’s back again,” Moyes told a news conference.
“It’s nothing down to me, it’s down to Jack Grealish. He’s looked after himself and worked incredibly hard.
“He’s come back with the right mindset to produce and he has produced for us. He’s made a big difference. It’s just the start for Jack.”
After making his Premier League debut for Aston Villa in May 2014, Grealish has now made 193 appearances in the competition and won the title three times with Manchester City.
Before joining Everton, he had provided two assists in the same Premier League game only twice before.
Grealish is the first Everton player to record multiple assists in consecutive Premier League matches and has the chance to be the first to do so in three when the Toffees host his former club Villa on Saturday at 15:00 BST.
He topped an eight-man shortlist after a public vote combined with those of a panel of football experts.
Moyes said it was a “big motivation” for Grealish to break back into the England team before next summer’s World Cup and his performances in the early part of the season have “put a marker down”.
“I don’t pick the England team and I’m glad I don’t because there’s so many good players,” added the Everton boss.
“They played really well against Serbia, some really good performances, so Jack needs to keep playing well for us to get ahead of them.”