Atsu arrived from Chelsea on a season-long loan but the Ghana international winger has struggled to make an impact at Goodison Park thus far.
The 22-year-old has been limited to appearances off the bench, though he made his first Premier League start against Leicester City last month.
Having spent last season on loan at Vitesse in the Eredivisie, Martinez has urged fans to be patient with Atsu as he becomes accustomed to life 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," Martinez told the Liverpool Echo.
"In other leagues referees allow less contact and they are a bit more protected.
"But 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.
"To be left-footed in that wing position with a real penetrative edge like he has can give you a big advantage."
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