A 1-0 win over Bournemouth at Goodison Park on Sunday meant Everton just about managed to stay in the Premier League on the final day of the season.
Everton have struggled on and off the pitch throughout and the poor results have mirrored the problems behind the scenes.
The fans have been at war with the board throughout the campaign and Moshiri’s running of the club has come in for massive criticism due to the way the club wasted money and brought in the wrong managers.
Stubbs conceded that a club of Everton’s size should not be celebrating surviving relegation on the final day for two seasons running.
He admitted that it would be a massive surprise if the current board are not removed as Everton need fundamental changes behind the scenes because the club have been a PR disaster this season.
The Toffees legend urged Moshiri to stop listening to people with no understanding of the club and allow professionals to do their job.
Stubbs said on talkSPORT: “We celebrated this last year, which I find incredible. You can’t be celebrating staying up for a club like Everton.
“There have to be changes.
“I’d be flabbergasted if not today or the next 24 hours there is a statement coming out of Everton football club about resignations because this board have to be dismantled.
“This club are too big and too great to be getting dragged through the gutter.
“For this season, some of the stuff that has come out of Everton has been a PR disaster.
“Labelling fans, wrongly accusing them of things – you couldn’t write it.
“Now that we have managed to stay up by the skin of our teeth again there has to be fundamental changes behind the scenes.
“There are divisions, everybody is not on the same page, the owner has to allow people to do their jobs and stop listening to people who haven’t got a clue.”
It remains to be seen whether Moshiri agrees to carry out changes behind the scenes over the summer and provide Everton with a fresh start.