A section of supporters chanted "You don't know what you're doing" after Wenger substituted striker Olivier Giroud for Francis Coquelin in the weekend's goalless draw against Aston Villa. With no trophy in seven years there is growing disaffection at the Emirates Stadium but Everton counterpart Moyes still thinks Wenger is the right man for the Gunners.
"Supporters want results but if you have got someone like Arsene Wenger in there you have to trust he is doing the right thing," said the Scot, whose side host Arsenal tonight.
"I believe 99% of Arsenal supporters think he is doing the right thing.
"It has always been a difficult job being a manager, although we are also in a privileged position.
"It is tough in different ways - there is a lot more that goes with it than what you see on a Saturday - but I enjoy it and I am fortunate I am at a good club.
"Criticism affects everyone but if you are in the business you have to accept you are going to get it.
"The job is to work through it and lots of times you don't need to look at it, read it or listen to it."
Arsenal were the last away team to win a Barclays Premier League match at Goodison back in March and the Toffees are now unbeaten in 10 at home. While striker Nikica Jelavic has suffered a dip in form with just one goal in his last six outings summer singing Steven Naismith, after a difficult start, has now scored in back-to-back games. He has three goals this season and all from within eight yards and Moyes hopes the Scotland international can develop into the penalty-box predator which will bring more goals to his side and ease some of the burden on his Croatian frontman.
"I always thought he could get some goals and the reason for bringing him in was to add more firepower and goals to the team," added the Toffees boss.
"You always think the real best goalscorers - and unfortunately I have to mention the other side of the city but Ian Rush, Robbie Fowler and John Aldridge - scored a lot of goals from inside the six-yard box.
"I think you have to get a big percentage of your goals inside the six-yard box or in off the goalkeeper in that area.
"Everyone needs goals in more abundance and you need to score goals from all different areas and different people."