The 19-year-old Spanish winger recently joined the Toffees on a season-long loan deal from Barcelona.
"We need to be patient as he's a young man, but in the same manner I think we can enjoy his quality," Martinez told the club's official website.
"He's decided to come to Everton and we need to look after him well. The warmth of our fans and Goodison will help him to grow, but clearly he's got the talent to help the team and we're really excited about Gerard's progress."
Deulofeu made his Everton debut on Saturday as the team lost 2-1 to Real Madrid in a pre-season friendly.