The Costa Rica international suffered a broken leg in an FA Cup tie with Stevenage in January and confirmed last Saturday that he would not return to fitness in time to feature at the World Cup finals.
Oviedo had amazed Everton with the quickness of his rehabilitation and looked to be on course to participate in Brazil.
Those hopes may now have been dashed, but manager Martinez believes Oviedo can take plenty of positives from the way he has fought back from the devastating injury.
"The disappointing aspect was that he picked up a really horrific injury, but now he is recovering really, really well," Martinez told evertontv.
"He made us believe that he was going to make the World Cup because it was incredible, the manner in which he recovered. Now the medical department has highlighted that it's a real risk for Bryan to go and his health is at risk.
"He's progressing well. It was an injury that at times takes up to 12 months to have the bones heal and after three and a half months he's already doing things that he's got no right to do.
"So we're really happy with the way he's progressing, even if the World Cup is going to be a disappointment."
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