Hernandez made just five Premier League starts during Moyes' ill-fated eight months in charge at Old Trafford, and the pair have been reunited after the Scot was confirmed as Slaven Bilic's replacement this week.
"He's a top goalscorer, a brilliant finisher," said Moyes of the 29-year-old who has started each of West Ham's 11 Premier League games this season, according The Guardian.
"It was difficult for him at United because I had Robin van Persie, Wayne Rooney, Danny Welbeck, Shinji Kagawa, so there was lots of competition. But he'll be treated the same here – if he's playing well and scoring, no problems. If he's not, it will be the same as the rest.
"They need to be there to say: 'Yeah, we know what we're doing.' Ultimately you organise them, do the work during the week, but then there is a responsibility. That's why the players are paid very good wages: they can't be looking round and saying: 'We want the manager to tell us what to do.' They have to have a bit of responsibility themselves."
The declaration is the second hint Moyes has dropped over his intentions in the transfer market after admitting he could supplement his squad with youth players rather than new arrivals, having been inspired by England's Under-17 and Under-20 World Cup victories.
If Moyes does indeed have plans for Hernandez to lead his attack - they face Watford in his first game in charge next Sunday [19 November] - he may have to wait to field the forward after Hernandez suffered a hamstring injury in Mexico's 3-3 friendly draw against Belgium.
Hernandez had earlier won a penalty on his 100th international appearance but only lasted 51 minutes as he went down clutching his left hamstring.
The ex-Bayer Leverkusen forward has undergone tests and will be rested from the friendly against Poland next week, returning to West Ham where he will be evaluated by the club's medical officials when the length of his absence will be determined.