The highly-rated 19-year-old has arrived on a season-long deal from Barcelona B and, while the forward has earned rave reviews playing for the Catalans' second-string team, Martinez does not want too much expectation placed on his shoulders.
"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 evertontv.
"He's decided to come to Everton and we need to look after him well.
"Clearly he's got the talent to help the team and we're really excited about Gerard's progress."
The Toffees are currently on a pre-season tour of the United States but Martinez is still trying to bring in more players to add to the four - goalkeeper Joel Robles, defender Antolin Alcaraz, striker Arouna Kone and Deulofeu - signings he has made so far.
Ajax defender Toby Alderweireld, who had been of interest to neighbours Liverpool and Premier League rivals Norwich, appears to be on the Spaniard's short-list.
"It's true that Everton have made an approach for Alderweireld," agent Soren Lerby is quoted as saying in Belgian newspaper Gazet van Antwerpen.
"But there are other concrete options. Toby will now have to decide which team he sees as the biggest challenge."
The Belgium international's contract with Ajax expires next summer.