The 19-year-old has arrived at Goodison Park on a season-long deal from Barcelona B, where he earned rave reviews, but 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."
Ajax defender Toby Alderweireld's agent Soren Lerby has confirmed that Martinez has made an approach for the 24-year-old Belgian.
"It's true that Everton have made an approach for Alderweireld," Lerby is quoted 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."