The Spanish midfielder looked back to his best on Saturday when Newcastle were defeated 2-1 at St James' Park. And Moyes is looking for more of the same on Wednesday night in the home Barclays Premier League fixture against Birmingham.
Moyes said: "I can think of a lot of players in the Premier League who haven't played as well as they should do. The players are looking for things to change and Mikel is the same. We have persevered with him, we kept believing in him. Over the last month or so there have been signs he is improving."
He added: "He is a terrific player who also has a little bit of a British heart as he understands the effort and the energy required to play in the Premier League."
Moyes has been left exasperated by his side's ability to blow hot and cold during an inconsistent season.
Their win at Newcastle came in the wake of a home FA Cup defeat by second tier Reading.
But should Everton chalk up a third successive league victory at the expense of Birmingham they will go eighth in the table.
Moyes said: "I want the players to show how good they are and go on a decent run and get a bit of consistency.
"Our players are always good at bouncing back and showing it matters to them. I think the resolve has always been there.
"It has been in the make-up over the years. But we do not want to be winning one game and losing one."
Source: PA
Source: PA