Moyes is leaving the Toffees this summer after over 11 years in charge to replace the retiring Sir Alex Ferguson at Manchester United, with the 50-year-old's final game as boss of the Merseyside outfit being this Sunday's Barclays Premier League trip to Chelsea.
Speaking at Everton's end of season awards ceremony, Moyes reflected on his tenure at Goodison Park and was keen to praise the efforts of those who have played under him.
"The memories I've got from Everton are going to live with me for a long time," he said.
"The character the players here have had is great. All the players in my time here have been great.
"I often think how lucky I am to not only have great players but great men. For that, I thank them all.
"I brought all the players in the current group to Everton, barring Ossie (Leon Osman) and Hibbo (Tony Hibbert).
"I take full responsibility for the players we have here and I've always wanted to give the players everything we can and tell them that we will be challenging at the top of the league.
"I always tell them we will keep getting better, and I believe we have.
"The group of players we have got are great. The way they work means they police themselves.
"On the training ground every day, they are the ones who demand it of each other and after my time, they won't allow it to change because there are too many players with the same approach. They know the standards we've set and what is required.
"Behind the scenes, we have former players in Alan Stubbs, David Weir and Duncan Ferguson back on the staff. And there will be more from the group there now because they are great lads."
On the current campaign - in which Everton are guaranteed a sixth-placed finish in the league - Moyes added: "I would like to thank all the players for the way they performed this season because they have been excellent all year.
"They've been in the top group in the table pushing all year, our home record has been excellent and the players have been brilliant for me - I couldn't fault them at all. I would like to thank them for everything they have done."
Moyes also thanked Everton supporters for the way they acted during his final Toffees home match, last Sunday's 2-0 win over West Ham.
The Scot received a rapturous reception from the home crowd at the game, and he said: "On Sunday I have to say I thought Everton showed great class in the way you treated your manager.
"But more importantly for me, in the second half you supported your club.
"You knew you were losing your manager but you supported your club. I admired that more than I have admired anything and I hope you keep supporting your club.
"I wish you all the very best for the future. Thank you."