But what will Martinez need to do as the first-team squad returns for pre-season training?
Here we look at a few issues which will need resolving by the Everton manager.
If there is one area where Martinez can prove himself to the Everton supporters, it is securing the future of left-back Leighton Baines.
The England international, 28, did not play for the former Wigan boss during his time at the DW Stadium, but he fits the template for the Spaniard's style of attacking football and is a potent threat down the left flank for the Blues.
That is unlikely to be the end of the matter, however, and Martinez must work hard to ensure Baines is not lured to United before the transfer window closes at the end of August.
Martinez's hopes may be helped by Baines' recent praise for the new Goodison boss, as Greg O'Keeffe of the Liverpool Echo noted.
While Baines may still be with Everton this season, only the most optimistic Blues supporter can envisage Marouane Fellaini remaining at the club.
However, Martinez must ensure he knows what the 25-year-old's intentions are well before the transfer window closes.
Everton saw midfielder Mikel Arteta join Arsenal in the closing hours of the summer transfer window in August 2011, as BBC Sport reported, leaving them unable to spend the £10 million gained from the deal until January 2012.
The Mirror article reports that a £23 million release clause will allow Fellaini to leave, which is a good chunk of potential transfer fees Martinez can use.
The prospect of Nikica Jelavic up front for Everton at the start of last season had supporters salivating.
However, after scoring four times in the opening six Premier League games, Jelavic scored only four more times all season.
Victor Anichebe displayed an improvement in form but is not the out-and-out goal scorer Everton need.
Wigan striker Arouna Kone, 29, has been strongly linked with a move to Goodison, as Simon Jones of the Daily Mail reported, but Everton also require a younger forward to develop and become a prodigious goal scorer the fans have been yearning for.
After Jan Mucha left Everton at the end of last season, Goodison goalkeeper Tim Howard has been left with no experienced cover ahead of the new campaign.
Slovakia international Mucha offered little threat to the United States international during his time with the Merseysiders, but did show some form when he stepped in for Howard for two league matches in March.
Now, though, Howard has even less competition to keep him on his toes and, at 34, is approaching veteran status in goalkeeping terms.
Finding a potential challenger to the current Everton No. 1 should be high on Martinez's list of priorities.
No job should be without some enjoyment, and Martinez can look forward to a potential flying start as he peruses the Everton fixture list for next season.
The Goodison boss will be pitting his wits against Juventus coach Antonio Conte in a preseason tournament in California on August 1, and can then look forward to a trip to Norwich on the opening day of the new season.
The game at Carrow Road represents one of seven winnable matches in the first nine Premier League games of Martinez's reign.
If the Spaniard can build up a head of steam in these games, he will find the supporters fully behind him and the ghost of Moyes exorcised immediately.