Deulofeu has not made a Premier League start to date this season, with every one of his four appearances coming off the substitutes' bench.
The Spanish winger admits he has become frustrated by his lack of minutes, but Martinez has been keen to make him aware that his chance will come later in the campaign.
"The manager had told me to be calm, that it is a long season and there will be a lot of opportunities to play," Deulofeu said.
"I have told him that I want to play now and I hope that I can play a lot more and help the team."
Deulofeu's quality is known at Goodison Park, as he impressed while on loan at the Merseyside outfit from Barcelona in the 2013/14 campaign.
In that season, the youngster showed his skill and provided Martinez's side with a potent outlet in wide areas, resulting in him making 25 appearances across the term.
Deulofeu is older and more developed now, too, and he may have hoped to have been thrust straight into the team after completing a permanent deal in the summer transfer window.
However, his best chances have come in the Capital One Cup so far. The 21-year-old played 90 minutes against Reading last week, and he scored in the fixture.
He will now be hoping that Martinez has seen enough to trust him to start in the league, with Everton facing West Bromwich Albion later this evening.