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 on Thursday night, 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."