Moyes will celebrate 11 years in charge at Goodison Park in March but the faith shown in him by chairman Bill Kenwright and the board is an increasingly rare commodity in football.
Some Everton fans have grown increasingly impatient with Kenwright's failure to secure more financial investment, but Moyes is in no doubt what he brings to the club.
The Scot said: "I don't know if we are scratching our heads any more, and that's probably the football world we're in. I'm not saying it's the right one, and I'm not just willing to brush it aside. But that's the way it looks just now.
"If you look at the clubs who have kept their managers for longer periods, I think that's tended to work better than continually changing managers.
"I do think I'm really fortunate because of the board I work for and the chairman I work for. At times they've had to show patience with me but I hope in the end people will look at it and say it's the right thing to do.
"I think stability brings a lot of good things. You have players who have been there for a while and you keep those players, it's not a constant change.
"And the money it costs to continually get rid of your managers and bring in new managers, you've got to be a pretty wealthy club if you're going to do that."