United this week failed with a £28m double bid for the Everton pair which was branded "derisory and insulting" by Moyes' former club.
And the Scot further annoyed his successor by claiming in an interview he would have "found it very difficult" to deny Baines and Fellaini moves to Old Trafford if he was still in charge at Goodison Park.
It is not yet clear whether United will return with an improved offer, but in the meantime both played in Everton's goalless draw with West Brom on Saturday.
And afterwards Martinez offered a clear rebuke to Moyes when he said: "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."
Martinez will continue to select Baines and Fellaini while they remain at the club regardless of the speculation.
He said: "We are focusing on every game and know there is going to be a lot of speculation every day because we are in the transfer window, but that is for the outside.
"Internally, we are working every day with real competition for places and just focusing on getting stronger as a team and making sure we can perform as well as we can."
Moyes signed Baines for the Toffees from Wigan for £6million in 2007 with Fellaini arriving from Standard Liege for £15million the following year.
United's offer for them is reported to break down as £12million for Baines and £16million for Fellaini, but Martinez does not believe Moyes would have considered selling them for such a price.
He added: "Everyone has got a price (but) when you invest money in a player and five years later you get offered the same money after performing really well, that becomes a little bit of a nonsense.
"The last thing I want is to get into a media war with a manager I really respect.
"As a new manager, I am following the structure we have at the football club. I heard in the past that Everton never sold cheap."
Everton are now bracing themselves for an improved offer from United for the pair but Martinez insists the club have never considered a fee they might be prepared to sell at.
He said: "Remember that the position we have got is we don't want to sell, so then you haven't got a figure.
"I am not going to go along with the circus the transfer window can become. It has been a bit of a farce really."
Martinez had no problem with the club going public over the matter after news of the bid had been reported in the media.
"The unfortunate matter is the offer was in the paper before it was made," he said.
"They did waste their time. When you put an offer that is below what you spend, I am sure you expect it to be rejected.
"That is a question you should put to the people who put the offer in."