The Toffees boss is pleased by his side’s character after bouncing back from a poor start to move up into seventh place, without the help of several injured key players
The Toffees endured a torrid start to the season which saw them flirting with the relegation zone, although they did mount an astonishing comeback at home to Manchester United where they scored twice in injury time to level the scores.
However, they have since transformed their season and are currently in seventh place in the table, where they are almost certain to stay.
Their latest victory was a 2-1 victory at home to Manchester City, where they came from behind to win thanks to a stunning header from Osman, a player Moyes believes does not get enough credit.
"I think the supporters recognise how good a talent he is," he told reporters.
"He has made the most of his ability. Technically he is a gifted little player.
"He is tenacious, he is tough and he runs as far as anyone in an Everton jersey every Saturday.
"He is valuable to us and is a key member of the team and the squad."
Injuries to key players such as Tim Cahill, Mikel Arteta and Marouane Fellaini, as well as the sale of Steven Pienaar to Tottenham have hampered the Toffees, but Moyes is delighted by their recovery after their early season slump.
He added: "We are really pleased. It is a good run to be on and something we should be talking about at the end of the season. We aim to try and keep that going.
"I never doubted our character and spirit. I didn't think that was the reason we weren't winning games.
"We have kicked on. We should never have found ourselves in the situation we were in but we did.
"It was difficult early on but the players have rallied round, showed their true value and how they can play.
"If we finish in seventh that would be great but we don't want to get caught by the teams behind us."