The Hammers have had a mix of results this season, and in their past three Premier League game have beaten Manchester United at home but also lost to Tottenham and Nottingham Forest in scorelines the club will want to forget.
Moyes told the BBC's Football Daily podcast that Lopetegui must be given time in order to implement his tactics and turn the club into a fighting force.
"I had a few defeats where we lost heavily at different times, so it happens for all managers," he said.
"I think the new manager coming in needs time and to be given that opportunity to set things the way he wants them to happen.
"They look as if they're a bit more open than they've been before and more liable possibly to concede. But they're desperately trying to score more goals as well.
"This time last year, I think we'd played about five or six more games than what they have just now, because we had the European competition to compete with as well. So the players there should be much fresher, bigger energy, showing that.
Moyes also admitted that some of the players have been underperforming and must show the Spaniard what they have got to offer this season.
"But I just think that the manager needs to be given an opportunity, a bit of time to settle things down. Sometimes players need to perform as well, they need to step up and show what they're about. I'm sure a few of them can play better and show the manager exactly what they can do."