Despite playing just 25 minutes of Premier League action so far this season, Martial has already notched two goals and an assist in the top flight.
His cameos have helped United to make a flying start to the new campaign, securing back-to-back 4-0 wins.
Martial is pushing hard to be included in United’s starting line-up but Mourinho still wants too see more from the French ace.
He said: “I think when you have some talent, you cannot waste it.
“I think when you’re blessed with some talent, you have to fulfil that talent, you have to explore that talent, you cannot be happy just with glimpses of talent.
"I want more from him because he has all the qualities for that.
"But I think he understands me better too and the personal relation [between us] is good, so again Anthony, I hope he’s going to better this season than last season."
Henrikh Mkhitaryan has also started the new season in impressive fashion, contributing four assists already.
The Armenian ace had a mixed first year at United but is starting to show his best.
Mourinho added: "I think Henrikh understands me, and to be honest, I understand him because in the beginning of [last] season if he understands me better, he would have started better.
"But at the same time, if I understand him better, I would probably help him in a faster way than I did.
"But, we spent our time together, working together, learning each other.
"The second part of last season was good for him and I believe with his talent that this season is going to be even better."
United welcome Leicester to Old Trafford tomorrow evening.
