Moyes believes he is in a privileged position at Goodison Park as his team prepare to face League One Carlisle in the FA Cup looking to go one better than last season when they were losing finalists to Chelsea.
He said: "I think I am at a really good club. You look at the way some managers are getting treated at present.
"I am really fortunate I am working with good people. Sometimes we have to be thankful for that. At Everton there has been a level of success because of good stability.
"We are a getting a big closer to winning trophies. We had a great run in the cup last season.
"Playing on the last day at Wembley was special and has given me a bigger hunger to do it again with a different result. That's why we are treating the competition seriously."