Manchester United saw a joint-bid for the Toffees pair knocked back earlier in the week, with former Goodison Park boss David Moyes rebuffed in his efforts to secure the services of players he knows well.
United's offer, believed to be in the region of £28million, was branded 'derisory', 'insulting' and 'a waste of time' by the Everton board and Toffees boss Martinez.
They hope the matter has now been brought to a close, with everything having gone 'quiet' on the transfer front.
Martinez is hoping to avoid another unsettling approach before the summer window closes, and the Spaniard has called on the relevant authorities to take action in order to prevent similar situations from arising in the future.
Asked if there had been any further movement on the transfer side of things at Goodison, Martinez said: "Everything has been quiet on that front.
"Everything has been as we have informed our fans. I think that is the way we are going to deal with the window now.
"We are still trying to be as strong as we can. If there is anything we need to inform our fans, we will do. But now the focus has to be the games.
"I have said it time after time, it's time for the football authorities to look into the situation.
"I think the transfer window is getting out of hand and really affecting the values of the league. I think it is affecting the human side of the players in a very, very unfair manner.
"It's about time that we stopped the window or we stopped the official games in the middle of the window."