The two stars were the subject of a rejected double bid from the reigning Premier League champion earlier this month, with the offer subsequently described as "derisory" by Everton. The Red Devils have reportedly submitted an improved bid for the duo, with Moyes urging Martinez to "do what [is] right for the players," but Martinez hit back on his predecessor at Goodison Park following Saturday's 0-0 draw with West Brom.
"I think my comment is quite clear," Martinez told reporters. "If managers start talking about players that are registered in other clubs, then 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, and I could easily come out and give my opinion about his players but I think I'll be more respectful than that.
"The position we've got is we don't want to sell. So then you haven't got a figure. Everyone has got a price, but when you see you invest money in a player and five years later you get offered the same money after performing really well, I think that becomes a bit of a nonsense.
"The last thing I want is to get into a media war with a manager I really respect. I think the business should be done quietly, but it's very unfortunate when you read papers and people talk about your players.
"I could sit down here and give you half an hour of my vision of how the other club is being run, the players that they want to go and how they should be sending all the messages to all the clubs around the world that they've been trying to sign players and they haven't been able to do it."
Regarding Fellaini and Baines' performance in the draw with West Brom amid all of the speculation, Martinez had nothing but glowing things to say.
"On the outside there's a lot of talk and speculation, but as you can imagine internally we are focusing on the games," Martinez said. "We need to concentrate on working hard and getting ourselves as good as we can. I never had a doubt because they are two professionals, they are two ambassadors of Everton, they have been here for a long time and they know how to perform and give everything they have."
The former Wigan manager also questioned the fairness of allowing the transfer window to overlap with the start of each new Premier League campaign, with three fixtures scheduled prior to its close on Sept. 2.
"I've said it a few times, I think it's very unfair to play competitive games when the window is open," Martinez said. "I hope the authorities will look into it, because it's going to get worse. You're looking at next season we've got the World Cup final on July 13 and the first league game on Aug. 7, you're going to have a full month of speculation.
"Many teams will have a starting XI on Aug. 7 and maybe five or six changes by Sept. 2 the way it's going."