England international Barkley produced a powerful run and stunning finish to open the scoring in the Premier League encounter at Goodison Park.
Kevin Mirallas' deflected free-kick and Steven Naismith's header made it 3-0, before Bobby Zamora netted a consolation for the visitors, who are yet to pick up a point on the road this season.
With the win propelling Everton into the top half of the table, Martinez was delighted with the display of Barkley, who was deployed in a slightly deeper role against Harry Redknapp's side.
"The big enjoyment of working with Ross is how quickly he takes concepts on and how quickly he experiments with different starting positions," Martinez told Sky Sports.
"The power and pace he has combined with that technical ability and ball control makes him special.
"Sometimes you get a really talented footballer that is skilful on the ball, or the powerful and strong [player] that can show that physicality on the pitch. He's got both.
"He's played that number 10 role, been getting into the box and having the freedom to find that space, but in a deeper position I think he makes very good decisions on the ball.
"The link-up play was very good at times and it's good for him at such a young that he experiments in different roles."
