Deulofeu's discipline within matches has sometimes been questioned, with the winger occasionally guilty of switching off in his defensive duties.
However, the Spaniard knows that he cannot afford to do that at Everton, and Martinez has warned him that he will lose his place in the team if he does.
“I know I need to be well positioned defensively and Roberto tells me that; if not, I won’t play," he said. "I’m learning, happy. And when I’m attacking I can take people on, cross, move. The main thing is to stay wide, opening the pitch."
Deulofeu has recently broken into Everton's starting line-up, after spending much of the initial part of the season on the sidelines.
Martinez seemed reluctant to utilise the youngster in the early part of the campaign, but he has forced his way into the Toffees line-up with a series of excellent performances.
Deulofeu has now started Everton's last three matches, and he will be determined to keep his place for the foreseeable future.
The Spaniard's next appearance could come against Manchester United at the weekend, where it will be vital that he is switched on defensively if Everton are to get a result.