Moyes will take charge of the Toffeemen at Goodison Park for the last time tomorrow when West Ham provide the opposition.
Victory may keep alive outside hopes of a place in next season's Europa League, for which Everton will have to finish in the top five.
And that knowledge alone underlines the progress Everton have made under Moyes' stewardship.
"When I took over we were bobbing along not far off the bottom of the Premier League," said Moyes.
"Now, it is a club that, on Sunday, will still be competing to be in Europe. That is a big thing."
It is one of the reasons why Moyes is adamant his own successor will be inheriting a job of immense promise.
And the 50-year-old has already offered chairman Bill Kenwright every assistance in trying to secure his replacement.
There was less than 36 hours between Sir Alex Ferguson announcing his decision to retire and Moyes' appointment as Manchester United's new boss, underlining the speed with which the United hierarchy wanted to get the succession issue settled.
For Kenwright, the process is going to take slightly longer.
Already Wigan's Roberto Martinez has been ousted as favourite by Neil Lennon, whose performances in the Champions League with Celtic this season offer an experience at the highest level even Moyes cannot manage.
However, such is the mature manner in which Moyes has handled his own exit, his relationship with Kenwright remains strong enough to have significant input, just as Ferguson did in United's decision to go after his fellow Scot.
"I'll help Everton as much as I possibly can," said Moyes.
"Walter Smith recommended me for the job here and if there is anything I can do to help Bill Kenwright with what happens next I will be more than happy to do so.
"It is a great opportunity. Everton is a well run club and we don't get ourselves into too much trouble.
"There is a brilliant training ground and a great set of players with a terrific attitude.
"Whoever comes in is coming into a really good environment."
The mature manner in which Moyes' exit has been handled is one of the reasons why there was never any real doubt he would be able to complete the final two games of the campaign, despite announcing he was joining a club Everton fans have not always been well disposed to.
The last player to make the switch to Old Trafford from Goodison Park, Wayne Rooney, received tough receptions whenever he returned - he was even abused by a sponsor on one occasion - although, after nine years, the ire has now quelled.
For Moyes though, it was important his exit was handled properly.
"Hopefully on Sunday the fans will react in the same way they did when I first stepped through the door," he said.
"You can never tell with football fans. They support their team and I would understand it if they weren't happy.
"But I will be standing in the same position as I always have done, trying to see if we can keep everything focussed and moving in the right direction."