Though the Manchester United manager will take on the Toffees for the first time since leaving for Old Trafford, his successor at Goodison Park plays down its significance.
The reigning champions welcome the Toffees to Old Trafford on Wednesday, with Moyes going up against the club he spent 11 years with before replacing Sir Alex Ferguson in July.
Though the Scot left on good terms, his relationship with the Everton supporters may have been tested by his purchase of midfielder Marouane Fellaini and failed pursuit of left back Leighton Baines.
"Football is not about the managers. It's about the players and the institutions. The two clubs facing each other is going to make it a great game," Martinez told reporters. "I don't think [the reaction to Moyes] 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."
Martinez has enjoyed a solid start to his tenure at Everton, guiding the club to fifth position with 24 points from 13 games, but warns his charges to "respect" United.
"We pay huge respect to the champions," he remarked. "You don't win this league unless you've got something special and we have to be at our best.
"They are the champions and we'll have to be well aware of their threat. It's a game where we need to perform well."