The Brazilian moved to Camp Nou from Santos in a reported €60 million deal over the close-season and has gone on to score four goals in 18 games since.
Lionel Messi's recent absence through a hamstring injury, and struggles throughout the season with his fitness, have placed more onus on Neymar to strike.
And while Martino remains content with the 21-year-old's performance levels, the Argentine wants a better return from his striker.
"He should score more goals than he has so far," the Barca boss said.
"We don't analyse any player simply by the goals he scores and lays on - it is a question of all facets of a player's game.
"But at the moment the only question about Neymar is his finishing.
"He is not a goalscorer in the way that Leo Messi is, but he can score a lot of goals for us like Pedro, Alexis Sanchez and Cesc Fabregas do."
Barca host Celtic on Wednesday in the final UEFA Champions League Group H game, looking to seal top spot with a win.
Martino is demanding high intensity from his players for the visit of the Scottish champions, whom they beat 1-0 at Parkhead on matchday two.
"We have to be precise and quick in our build-up play and have to be effective in the way we move the ball about," he added.
"We also have to be precise when we press for the ball to evade the possibility of Celtic playing on the counter attack. It is important to put in a good performance - improving our performance is an obligation we have got."
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