"We want competition for places. We do not have many but there are 17 or 18 players who at the moment are competing so well.
"They're all up to full steam, there is lots of confidence and self-belief among them and we will try to keep that going for as long as we can."
The Everton manager is refusing to comment on Steve Bennett's decision not to rescind Tim Cahill's second yellow card at Manchester City, which forces the midfielder to miss the Middlesbrough game through suspension.
But Everton will seek clarification from the Professional Game and Match Officials Board on the issue of goal celebrations after comments made by general manager Keith Hackett in July.
Moyes said: "Keith Hackett has confirmed to me that he did say at the start of the season referees would not book players for that type of celebration. We know exactly what Keith Hackett told us.
"We went off that ruling and if he's the boss of the referees I would think they would take their orders from there."