The Toffees have started life under the new manager well with five wins from their first nine games, and the former Wigan boss believes his team will continue to improve with time.
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."