Here are the key lines from his news conference:
Thomas Soucek is unavailable, as the club are following the Premier League's concussion protocols following his incident against Brighton last week.
On James Ward-Prowse's impressive start, Moyes said: "One of the reasons we brought him here was his Premier League experience. He's come in and settled in really well for us. He has scored goals and created goals for us already and we're really happy with him."
Moyes says West Ham's away form will be "key" to maintaining their strong start to the season: "It's only the start of the season so we won't get carried away, but getting points and away victories has been difficult in the last season. Our form at London Stadium has been good, but we've only had one chance to do that this season. Away form will be key."
Reflecting on his time at West Ham so far, Moyes said: " I said when I joined that I wanted to grow the club and make it better, and I think we might have done that. We finished sixth and seventh in the league, and then won a European trophy, so I hope my time here will be seen as really positive."
On the upcoming Europa League draw, Moyes said: "We want to enjoy the trips, and I hope the supporters do as well. Going into it as Conference League winners lets us stick our chests out a little bit more."
On Luton, Moyes said: "Going to a newly-promoted team for their first home game of the season is always tough. All I can do is go and get my team ready as best I can, make them aware of Luton's qualities, and I'm sure Luton will use the tight environment to their advantage."