Unwilling to negotiate his future until the summer, there's already an unstable feel around the manager's position at the club, with many speculating he will leave in the next few months.
Achieving Champions League football was the only way most conceived him staying any longer, and with that now a fading reality, it seems increasingly likely Moyes will step aside.
Despite the high regard held for him by the media and the general level of respect he commands from fans, this is not an eventuality all Evertonians are dreading.
However, while some supporters may feel it's time for a change, this is not something the Toffees' hierarchy should readily accept.
Apart from two seasons, and the year they actually made the Champions League, Moyes has kept Everton competing between fifth and eighth throughout his tenure—tantalisingly close to breaking into the top four.
Not only is this consistency so impressive, but the teams Everton have remained competitive around manage significantly higher wage budgets and have far more financial freedom to spend.
According to Financial Fair Play, Everton's wage bracket is just below the average in Premier League terms, around £60 million, while top-six sides carry at least 50 percent more, with most doubling it.
Considering this and where Everton were when Moyes took charge—languishing in and around the relegation zone—the transformation to perennial top-six challengers has been immense.
His problem now is that his side are no longer improving, and without any form of investment Moyes is struggling to maintain the Toffees' previous high standards.
This was the case a year ago before some canny work in the 2012 January transfer window injected his squad with some much-needed momentum. Sadly that wasn't the case this year.
With Everton no longer visibly advancing, suddenly all his mistakes, his occasionally negative tactics and selection choices become overly highlighted; however, this only masks the main financial issues.
Getting his side where he has with such limited means is impressive enough, taking them into the top four on this budget would be simply miraculous.
Moyes had the Toffees in and around the top four for two-thirds of this current season yet, when his side needed that extra boost to maintain their challenge, as mentioned, the board came up short in January.
Another concern is the alarming lack of managerial pedigree tipped to replace Moyes, if he does indeed leave. Wigan's Roberto Martinez tops the betting (according to Skybet), a manager who has prospered on a limited budget yet is more accustomed to fighting relegation scraps than competing for Europe.
Behind him comes the untried duo of Steve Round and Phil Neville, who would surely be out of their depth taking a first management job at a top-six club.
Elsewhere, the likes of Mark Hughes, Martin O'Neill and Sam Allardyce crop up, but would surely be unhappy at the lack of financial support and, if sections of supporters chide Moyes' approach, best of luck stomaching that particular trio.
Michael Laudrup and Slaven Bilic are more fashionable choices, but plenty of managers have enjoyed similar initial success as Laudrup before fading away, while Bilic would be new to managing in the Premier League.
Quite simply, there are few attractive options and none on the same level as Moyes.
Considering the club's lopsided business model that relies heavily on the manager competing well beyond their means, it's imperative Everton fight hard to keep their man.
Where do you stand on Moyes' future at Everton?
It is still possible Moyes signs on, perhaps inspiring himself after masterminding some FA Cup glory or returning the club to Europe; however it still feels more likely he will opt to move on.
Moyes may not be the most attacking manager, and there are certainly times he has erred in judgement, as all managers do, but his record at Everton speaks for itself. If these traits remained after a time when he was financially backed, perhaps there would be more questions to ask.
It's true his current contractual situation cannot be having a positive effect on the team, which is certainly an issue fans are entitled to resent, yet the majority of frustration should be targeted at the continued lack of investment.
With the club's current resources, considering the sterling work he's already done and the lack of many viable alternatives, Moyes is by far the best man for the job.
Had he been backed this January, or at several other points during his tenure, who knows where the Toffees would be now under his charge. It's certainly far less likely he would be contemplating his future.