Everton quickly rejected the offer, describing it as "derisory and insulting".
Moyes, who left Goodison Park this summer after 11 years in charge, then claimed that he would have "found it very difficult" to deny Baines and Fellaini moves to Old Trafford if he were in Martinez's position, but Martinez believes that Moyes should show his former club more respect.
He told reporters: "If managers start talking about players registered with other clubs that's the end of the whole thing.
"I think everyone should look after their own things internally. I'm sure they've got many issues in the same manner.
"I could easily come out and give my opinion about his players, but I think I'll be a bit more respectful than that."
Baines and Fellaini both played 90 minutes as Everton drew 0-0 with West Bromwich Albion on Saturday.