The winger joined the Toffees on loan from Chelsea during the summer, but he has been used sparingly so far by Martinez.
However, Martinez believes that the 22-year-old has now started to adapt to life in the Premier League.
"We need to give him a little bit of time to adapt to the physicality of the Premier League just like any player but especially a winger. In other leagues referees allow less contact and they are a bit more protected," the Everton boss told the Liverpool Echo.
"I think the way he has adapted to the way we want to play so far has been impressive. He's an intelligent footballer. It's just making sure I can give him the right introduction to his role.
"With the minutes he's had so far in the Europa League and other games he's done well. I expect him to be himself in the second half of the season and he can be a very important player for us."
Atsu has made four appearances in all competitions this term.