In the summer the Spaniard replaced the Scot after he ended his 11-year association with the club to succeed Sir Alex Ferguson at Manchester United.
At the time the number of dissenting voices was considerable with the argument being that despite winning the FA Cup - something Moyes never achieved in his time at Goodison Park - a man who had overseen Wigan's relegation from the Barclays Premier League was not the right fight.
Fast forward a few months - during which Moyes has tarnished his relationship with Everton supporters after making derisory bids for midfielder Marouane Fellaini and, more significantly, fans' favourite Leighton Baines - and the situation has been flipped on its head.
Martinez, with his refreshing brand of attacking football, has guided the Toffees into fifth just three points behind second-placed Chelsea and significantly changed the atmosphere around the club even though he did eventually sell Fellaini to the Red Devils.
By contrast Moyes is perceived to be struggling at United and his transfer strategy - bidding £28million for Fellaini and Baines just a short time after the expiry of the former's £23.5million buy-out clause - has tainted the opinions of some Everton fans.
Martinez, however, insists Wednesday's game should remain focused on the players.
"I know that from the outside this is an attractive proposition to speak about the managers," he said.
"But football is not about managers, it is about the players and the institutions and two football clubs with incredible tradition facing each other is going to be a great game.
"We pay huge respect to the champions - you don't win this league unless you have something special - and we will have to be at our best to compete but we have to be ourselves."
Asked how he thought Moyes was now perceived on Merseyside the Spaniard added: "I don't think that is something that I spend much time (thinking) about.
"I think David Moyes did a fantastic job over the last 11 years and that is what I want to keep.
"Everything else that has happened are normal situations which would occur in football
"From our point of view I will always look at Everton in terms of getting stronger and progressing internally and on the pitch and I think we have done that in the last five months.
"It is not our style to look elsewhere (at other clubs and managers).
"We want to assess ourselves what we do internally, not having to look elsewhere."
United continue to be linked with a renewed bid for Baines even though the England international is sidelined possibly until the new year with a broken toe.
"He is progressing really well, better than we expected but we don't know (how long he will be out)," added Martinez.
"We know it could go up to six weeks but knowing Leighton it could be a lot closer.
"It is one of those situations where we have to take it day by day."
The comparisons between the two clubs do not stop at the managers or their transfer targets with Everton's precocious teenager Ross Barkley already evoking memories of a fellow academy graduate Wayne Rooney.
Martinez, however, said it was unfair to label the 19-year-old as the next Rooney.
"It would be a big mistake to compare players of that quality," he added.
"Ross deserves his own identity and his own uniqueness in the way he plays the game.
"Once Ross is 35 or 36 he can look back at his career and you can make comparisons.
"Wayne Rooney is one the best footballers of his generation and Ross has the same potential to do it in the future.
"But if you compare the two players you will make a mistake as they are very different and unique in their own right."
- Sports & Recreation
- Marouane Fellaini
- Leighton Baines
- Manchester United
- David Moyes
- Barclays Premier League