The last-minute defeat at Norwich City on Saturday appeared to be acting as potential metaphor for the Blues in the current Premier League campaign.
Things were going so well in the first part of the season that the Goodison Park club were touted as favourites by some to finish in the top four and claim a lucrative Champions League spot.
However, while recent seasons have seen the Blues find title-winning form in the final months of the campaign after a poor start, the opposite has occurred this year.
Four wins from their opening six league matches suggested something was in the air for the blue half of Merseyside. Nikica Jelavic had continued his rich goal scoring form from the previous season while Fellaini, Leighton Baines and Steven Pienaar were continuing to create chances.
However, a run of seven draws from nine league matches between the start of October and December put a spoke in the wheels of the team's progress. With the form the team had shown, though, this was considered a midseason blip and Everton would soon return to winning ways.
Sure enough, Moyes' side would take maximum points from four matches out of six before and during the Christmas period to re-establish themselves as top-four contenders.
Even hopes of finishing above Merseyside rivals Liverpool for the second successive season are beginning to waver even though the Anfield side are in a period of major transition under Brendan Rodgers.
Indeed, ahead of the FA Cup fifth-round replay against Oldham Athletic at Goodison Park tomorrow, Everton supporters can be forgiven for wondering what exactly the end of a season, which had promised so much, has in store for them.
Too many draws from winning positions and dominant possession have seen a slump in optimism on the terraces. Points dropped in draws with the likes of Swansea, Fulham, QPR, Southampton and Norwich, coupled with defeats at Carrow Road and Reading from winning positions, are hurting hopes of finishing in the top four.
Everton have now lost 19 points from winning positions this season.
So where has it gone wrong for Everton? The collapse of the proposed signing of Leroy Fer from FC Twente during the January transfer window has been a significant indicator.
A year ago, Moyes brought in Jelavic from Rangers for £5 million and the Croatia international helped to transform Everton's season with a slew of goals.
This year, though, the haggling over a knee problem with Holland international Fer saw the club attempting to alter the arrangement of the deal, which was subsequently called off. It is worth noting at this point that Fer has been playing regularly with Steve McClaren's team since January.
Instead, Moyes had to go with what he had in the first team, although the arrival of defender John Stones from Barnsley was tucked away as one for the future.
But with £8.6 million set aside for Fer, there appeared to be no contingency plan for any potential collapse of the deal for the Dutchman.
Moyes has often been accused of protecting a lead rather than chasing a second goal, the worst case of this perhaps being the FA Cup semifinal against Liverpool last season when Jelavic became more and more isolated up front, allowing the Reds to get on top in the second half of their eventual 2-1 win.
Jelavic himself has scored just twice for Everton since Nov. 10, with one of those goals coming in the FA Cup third-round 5-1 win at Cheltenham of League Two.
Like any striker, the 27-year-old was due a lean period, but the length of his current barren spell is a worrying statistic for Everton supporters whose hopes were raised by his form last season.
More pertinently, there is little threat elsewhere in the team despite the best efforts of Victor Anichebe.
Fellaini is Everton's leading goal scorer in the Premier League with 10 to his name, but there is a big fall-off until you reach Jelavic on six and then Anichebe and Baines one strike behind the Croat.
In light of all this, nobody can really argue with Moyes if his recently revealed interest in German football and his wish to leave his contract decision until the end of the season are intended as "fishing trips" for a new job.
One has to question how long the former Celtic defender can keep pulling rabbits out of wafer-thin hats at a cash-strapped Goodison Park.
Tomorrow night's visit of League One strugglers Oldham will go some way to answering that question.
The Latics have stunned Goodison before when Gary McDonald hit the only goal of the game with a spectacular strike in the 2008 FA Cup third round.
A similar outcome on Tuesday may hurt more than just Everton's pride in a season which promised so much but is perilously close to collapse.