The Ghana winger arrived on a season-long loan from Chelsea on Wednesday, having spent last term with Vitesse in the Eredivisie.
And, while tipping his latest acquisition to make a big impact, Martinez believes the step up in quality could lead to a period of transition.
"He's the sort of player that you always want to see him involved with the ball," the Spaniard said. "He's got that unpredictability in his play.
"I do expect a bit of an adaptation period. He hasn't played in the Premier League so that always comes with an adaptation period.
"Physically he's in a good moment, it's more just helping him adapt to the needs of this league.
"I'm confident it's going to be a short period."
Atsu, who started his professional career with Porto and featured for Ghana at the World Cup in Brazil, sees his temporary switch to Goodison Park as an opportunity to prove his worth in the top flight.
"This is my first season in the Premier League. It's a high level for me, and a good chance to prove myself." he said.
"It was a really great experience for me to play in the World Cup and it will continue to help improve my confidence in the Premier League."
Romelu Lukaku made a permanent switch to Everton from Chelsea during the close-season, having spent last year on loan on Merseyside, and Atsu refused to rule out extending his stay on Merseyside.
"At the end of the season we will see what is what," he added.
Everton get their season under way against Leicester City on Saturday, and Martinez revealed anticipation was building for the new campaign
"You can feel a completely different excitement this week," he said. "You get ready for start of the season and that's what we had from Monday.
"Today, Christian [Atsu] arriving gives us an extra option and a boost in the squad.
"The group are a year older, a year wiser and more experienced in the way that we want to play."
