Martinez has brought in three new faces so far this summer raiding his old club Wigan to sign Arouna Kone, Joel Robles and Antolin Alcaraz.
Distin has been impressed by how the new trio have settled in at Everton and feels the competition in the squad is strong enough to start the new season without anymore new additions.
"The competition is there because it is a much bigger squad now and we do not need any more players," Distin told The Sun.
"We have got three quality players in, which is great as we normally have a small squad.
"The new guys have felt at home from the very first day.
"It is really easy to settle down in a team like Everton because we're a good group of guys who welcome anyone without a problem."