Wigan drew 2-2 with the Toffees at the DW Stadium but the visitors' boss was left unhappy with the lack of protection afforded to Marouane Fellaini as well as Arouna Kone's goal
The most notable point of controversy came when Arouna Kone opened the scoring from what appeared to be an offside position but Moyes also complained about the lack of protection afforded to Marouane Fellaini.
The Scottish coach suggested that Martinez's comments in the build-up to the fixture had an impact on the performance of the referee and his assistants.
"I think Roberto has done a good job over the last few days of making sure that the referees gave them what was required," Moyes told reporters.
"We found it really hard to play against Wigan and we also found it hard because of the way the decisions went.
"I think Fellaini needs more protection. He is just standing there and they are standing on his toes. Their first goal was half a yard offside. The linesman should see it and it's up to them."
Moyes confirmed that he could speak to referees' chief Mike Riley about the performances of Kevin Friend, John Flynn and Mark Scholes.
The 49-year-old suggested, however, that Riley should take the initiative and scrutinise the job done by the trio at the DW Stadium.
"Yes, we can approach Mike Riley, and I'm sure others are," he added. "But Mike Riley has to look at the people who are working for him and whether they are doing well enough."