The Three Lions have been consigned to their earliest elimination from a finals since 1958 after losing their opening two Group B games to Italy and Uruguay.
Toffees pair Leighton Baines and Phil Jagielka have seen their international pedigree called into question, while Ross Barkley has been restricted to appearances off the bench despite being tipped to star.
However, Everton boss Martinez insists that he remains proud of his contingent of England players, and stressed that he will do his best to ensure that Barkley, John Stones, who was included on Roy Hodgson's standby list for the tournament, and future Goodison Park talents have "terrific" international careers.
He told the club's website: "From our point of view, we always pride ourselves on helping the England camp as much as we can in producing good youngsters and making as many available as possible. That will always be the case.
"It's always good to see players from Everton representing the national team and in the case of the youngsters, we're very excited about the ones we have.
"We're going to protect and develop John, Ross and the others underneath to fulfil their potential because they're going to have a terrific future for England and the English game in general."
Hodgson has confirmed that Barkley, 20, will start in England's final game against Costa Rica on Tuesday.