The former Wigan manager is expecting changes to his squad when the transfer window opens, but will not be forced to part company with the promising English pair
Barkley has earned his first England caps this season, with a place in Roy Hodgson's World Cup squad looking an increasing possibility, while Stones has also drawn plaudits for a series of exemplary displays in Phil Jagielka's absence.
The duo's performances have sparked rumours of moves away from Goodison Park, but Martinez described the rise of the young players as the club's "biggest success story" this term and insists the club do not need to sell their prized assets.
"The biggest success story of our season has been the development of our young players," said Martinez at a general meeting for Everton shareholders.
"For me, it is extremely exciting to see how players like Ross Barkley and John Stones have developed and that will continue to be central to what we want to achieve here.
"As long as young players are treated the same as the guys who have played 500 games, then they understand that there is a learning process, and that they have to keep improving. It is easy to motivate them in that way.
"The one thing everyone needs to know is that we are not in need of selling players. If we sell, it will be because the time is right and the squad will be in a stronger position because of it.
"What is important as a football club is that you don't have to sell to survive. That is not going to happen.
"Will there be new faces coming in and going out? Of course. With every window we need to get fresher, we need players coming in. But we do not have to sell."