The Spanish winger, who caught the eyes of many while 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 in the Guinness International Champions Cup.
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," Martinez 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."