Moyes reached the 11th anniversary of his appointment at Goodison Park this week but there has been little celebration following last Saturday's shock FA Cup quarter-final loss to Wigan.
A section of fans voiced their displeasure after the defeat and there has since been more speculation over Moyes' future with the Scot's contract due to expire at the end of the season.
Reflecting on his time in charge in his programme notes for the Toffees' Barclays Premier League clash with Manchester City, Moyes said: "I believe so much has changed since that very first game.
"The progress that the club has made since then can by shown by Everton's Premier League standings, when in the last 10 seasons we've finished outside the top 10 only twice.
"I understand this will never satisfy everybody and nothing would give me more pleasure than to bring the success that Everton had in the 1980s under Howard Kendall, with the great players that played for him.
"We are striving to reach those levels and we put every ounce of effort into trying to get back to that standard."