The reigning champions welcome the Toffees to Old Trafford on Wednesday, with Moyes going up against the club in charge of whom he spent 11 years 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.
But Martinez told reporters: "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.
|17/1||Everton and Manchester United are 17/1 with BetVictor to draw 2-2|
"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."