The season ended without silverware again for the club and, more notably, Moyes.
But there was also the disappointment of missing out on European football next season despite the team challenging for a Champions League spot throughout the season.
However, this was not a forgettable season for Everton supporters with several highs across the campaign.
Best performance of the season
One of the best displays of the season came in the opening match with Manchester United left shell-shocked by the defeat at Goodison Park.
Fellaini was the star man as he provided the impetus for a great start to the season, which also included an impressive 3-1 win at Aston Villa.
But the best performance of the 2012-13 was, arguably, the 3-0 win at Swansea City on Sept. 22.
Everton were simply irresistible in attack on the day with Victor Anichebe and Kevin Mirallas putting the Blues 2-0 up before halftime.
The Welsh club, who had enjoyed a fine start to their campaign with a 5-0 win at QPR on the opening day and a three-goal defeat of West Ham, had no answer to Moyes' team.
Nathan Dyer might have been sent off in the 58th minute, but it mattered little with Everton in such imperious form.
Fellaini added the final goal eight minutes from the end, but despite the occasional error at the back which saw Tim Howard work hard, Everton were in control.
Player of the season
But the destination of the award has to be Everton and England left-back Leighton Baines.
The former Wigan Athletic defender has again been at his best this season after reuniting his partnership on the left flank with Pienaar for the first full season since the South African returned from Tottenham.
The 28-year-old provided five goals in the Premier League this season and added five assists to his tally in a campaign which included an 82.3 percent pass completion rate, according to WhoScored.com.
Baines won the Everton Players' Player of the Year and Player of the Season prizes at the club's awards night to the surprise of absolutely no one, per EvertonFC.com.
Young player of the season
Everton midfielder Ross Barkley finally began to make his mark on the first team in the closing weeks of the season after spending the opening half of the campaign on loan at Sheffield Wednesday in the Championship.
The 19-year-old then spent a month on loan with Leeds United before returning to Goodison Park in February.
Worst moment of the season
The Capital One Cup defeat at Leeds United was dreadful. Played out in front of a live television audience in September, Everton were a team in decent form and the competition represented a good opportunity for the team to break an 18-year wait for silverware.
Everton, though, turned in a woeful display at Elland Road as Neil Warnock's team ran out comfortable winners.
But that was not the lowest of the low.
Everton were widely expected to see off the challenge of Wigan Athletic in the FA Cup quarterfinals in March and fans were already preparing for a trip to Wembley for the last-four stage.
The Latics were struggling against relegation and few could see a surprise coming.
But in the space of four first-half minutes, Everton pushed the self-destruct button as Maynor Figueroa, Callum McManaman and Jordi Gomez scored to leave Goodison Park deflated.
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