Martinez succeeded Moyes when the Scot left the club last summer to replace Sir Alex Ferguson at Old Trafford.
The Toffees have enjoyed a strong season in the league under the Spaniard and Moyes has been quick to praise the job that his successor has done.
"First of all, the game is not about me, it's about Everton and Manchester United," he told reporters. "I go there as manager of Manchester United and I'm delighted to be that. I was proud to be manager of Everton at that time but my job now is to make sure I get a result for United.
"The Everton fans were always terrific in my time there – very supportive and always right behind the team. We go there with a great away record and go there trying to keep that going. I know the players at Everton – they are a great group of lads and great professionals who got on with the job and were self-motivated.
"Over the years, we continued to add players there and it was a great group of young players. The senior group there is very important too. Roberto Martinez has done a brilliant job this year. He's got them playing well and in a good, healthy league."
Manchester United are currently seventh in the Premier League table, nine points behind fifth-placed Everton.