Moyes is currently tasked with moving the East London outfit away from the relegation zone, but the Scot has indicated that he wants to establish the club higher up the standings.
West Ham have gained points from Chelsea, Arsenal and Tottenham Hotspur since Moyes's arrival, and he wants to see similar levels of performances on a consistent basis.
The 54-year-old told BBC's Football Focus: "I've got an idea in my head how I want it to look. I want us to go to those teams and say, 'we're having a game with you and we're going to see if we can beat you.
"At the moment, we just don't have the same level of quality of players as those teams do, but I'm saying that for probably every other team bar the top six or seven in the Premier League."
Moyes has registered three wins and five draws from 13 matches at the London Stadium.