Moyes joined the club in November and Cresswell feels the approach taken by the Scot has paid dividends at the London Stadium.
"We feel well-prepared for every game," he told the club's official website. "That was the manager's thing from day one, that if you don't work hard and put your effort in for the team, your teammates, the manager, the staff and everyone here, it's clear you wouldn't play.
"I think he set his stall out well and everyone understands what their role is and what the job is and you could arguably say we're a lot more organized going into a game.
"The performance analysts work tirelessly to make sure we're well-prepared and well-organized for every game."
The Hammers have managed 20 points in 12 games since Moyes took charge and are now four points clear of the bottom three with betting sites which have odds for the Premier League suggesting they should now avoid relegation.
However, Cresswell is well aware they still have plenty of work to do to preserve their top flight status.
He said: "Twenty points in 12 games is a good return and certainly since the new manager has come in, we've had a turn in fortune and some good results.
"We didn't get off the best of starts at Watford and Everton, but 20 points from our last 12 games is a good return for any manager.
"It's certainly not over, though, and we have eleven games to play and a lot of points to play for, so we've got to keep pushing and striving and hopefully we will be OK."