The Toffees have endured a number of injuries to key players in the first few months of the campaign but the continues good form and emergence of talented quartet John Stones, Romelu Lukaku, Ross Barkley and Gerard Deulofeu has helped guide the team into the top half of the table.
Despite the fact three draws on the trot have seen Everton slip down to 10th position, Martinez believes there is enough quality at Goodison Park to see them push towards the pointy end of the table by season's end.
"We have had a lot of injuries throughout the season as any team has but I thought we coped really, really well," Martinez told Sky Sports News HQ.
"The young players showed a terrific attitude and personality to step in and do a really good job. Now the next thing is to become better in every aspect of our performance.
"But we are showing exciting signs and signs that I feel could take us into a special level."