The Mexico international wants to start for the Premier League champions but insists he relishes the competition for places up front
The 25-year-old has featured from the start in only two games for the Premier League champions this season, with Danny Welbeck, Wayne Rooney and Robin van Persie all afforded more minutes.
Hernandez insists he has the ability to feature regularly under Moyes but maintains he need to be given more chances by the United manager.
"I strive for that, I am working towards that, earning a spot as a starter," the striker told Telemundo.
"I know that my performances on the pitch will allow me to achieve that goal someday either here [in Manchester] or elsewhere for any other club.
"I just need to be given more opportunities to showcase what I can do, because all of us want to be able to contribute our part so this team can win championships.
"I am going on four years here [at Manchester United] and really, like I have always said, I am happy to be able to play for one of the best clubs in the world. So I’m happy, doing my best every single day to earn more minutes on the pitch."
Hernandez says he relishes the opportunity to compete for a place alongside Rooney and Van Persie and believes performance levels are raised when players are fighting for a spot in Moyes' side.
"Of course. What better way to compete anywhere in the world than to compete with them?" he said.
"The competition inside the team has always been really healthy and I think that helps the team a lot, because there are so many quality players that every one of them wants to earn a starting spot.
"The practices and matches coming up will force us to step up and help the team grow both at an individual and collective level."