The Merseyside club have made a solid start to the new Premier League campaign in Martinez's first term in charge at Goodison Park, sitting sixth in the table after Saturday's 2-0 triumph away at Aston Villa.
The next few weeks will represent a real test of their ability to keep pace with their fellow top-four contenders with games against Tottenham, Liverpool and Manchester United on the horizon, but Martinez is confident they can continue to gel as a unit.
"We have got a really good start behind us," he told Sky Sports News.
"We have a special group of players with terrific support and every game is a unique opportunity to enjoy our football and take as many points as we can. But we are still developing and growing.
"It is early days but everyone has played a massive role in a good start and we want that to continue."