The French international has enjoyed an excellent start to the new campaign, scoring six times in 15 games in all competitions so far, as well as laying on six assists.
That form has earned his a recall to the France side for their upcoming friendlies but whilst he is playing well, Martial says that he is keen to keep improving.
Speaking to United's in-house TV channel 'MUTV', the 21-year-old said:
"At the moment, I'm happy, even if I could have done more, scored more goals and made more decisive passes.
"I think the difference is that last year I didn't have a good season but, for now, things are going pretty well.
"I'm achieving my objectives and I hope to score a lot more by the end of the season.
"I must continue to keep up good performances for my club and if I've got the chance to start over there [for France) I will do the best I can."
Mourinho's respect for Marcus Rashford has led to Martial being forced to play the role of super-sub more often than he would have liked, as shown by his late introduction and winner against Spurs last week, but the youngster say that even if he is forced to start on the bench, he will look to come on and affect the game.
"I think when I come on to the pitch as a sub, I'm hungry, desperate to play," he explained.
"I want to get some action, to score, to make some key passes, I want to give everything I can to help the team."