The Spaniard has praised the 19-year-old's commanding performance at Carrow Road but claimed his side conceded "soft goals" against Chris Hughton's men
The England Under-21 international’s career has been dogged by injuries, but following an eye-catching pre-season, he justified a place in Martinez’s starting line-up at Carrow Road.
After Norwich went ahead through Steven Whittaker, Barkley hammered a shot past John Ruddy to equalise, before goals from Seamus Coleman and Ricky van Wolfswinkel ensured it ended all square.
"Scoring goals is the hardest thing in football and Ross has the talent. What I’m pleased about with Ross is he wants to learn, develop and listen," Martinez said.
"To have a player of that ability at that age is an incredible asset for us. He was perfect today.
"Many people will speak about the quality of the goal, but that’s something he does every day in training. I’m most happy about is his overall contribution.
"Tactically, he was outstanding and he worked very hard for the team. It was a very mature performance.
"I’ve seen that a lot in pre-season and he showed he is willing to help the team. He was excellent and he deserved his goal."
Martinez was buoyed by his side's creativity against Chris Hughton's men but insists his players must improve on their organisation in defence.
"I was obviously pleased with the chances we created," Martinez said.
"We all know that Norwich at Carrow Road are a difficult unit to break down, so I couldn’t be happier with the manner in which we were patient in our build-up, we created good chances to score good goals from open play.
"Overall, I’d say we deserved the three points but we conceded two soft goals, which is the area of the performance in which we need to improve."