The Spanish winger, who caught the eye playing for the Camp Nou side's B team last season, featured for the Toffees for the first time as a substitute in a friendly defeat against Real Madrid on Saturday night.
And after being impressed by his cameo against the Spanish giants, Martinez called for the Merseyside club's support to offer Deulofeu encouragement as he adapts to English football."We need to be patient as he's a young man, but in the same manner I think we can enjoy his quality," he told the club's official website.
“You saw a flash of his undoubtedly special talent [against Madrid]. 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."