Monday night’s 2-0 win means the Hammers now sit two points shy of fourth-placed Chelsea with a game in hand on their London rivals.
Jesse Lingard and Craig Dawson struck in the first half before Leeds wasted plenty of chances after the break. Lukasz Fabianski, back from injury, made two fine saves but Patrick Bamford twice let the Hammers off the hook.
After a nine-day break the hosts were slow out of the blocks too, but held on to respond after midweek results saw them drop out of the top four.
"Everybody says Leeds are a good watch," said Moyes. "It's a difficult game against them. We were fortunate at times but a little unfortunate at others.
"Not a good performance by our standards. The players are disappointed.
“Leeds United do a lot to you and make it difficult to play. You need the forward players to play well. We didn't do that well enough.
"We were resilient, we didn't play well tonight. I don't think Leeds help you play well, you have got to earn it.
"Leeds make you play at incredible intensity. All clubs when they play Leeds, their running stats will be as high as any time in the season.
"When you get near the top it gives you a big incentive. I was gutted when we dropped out the top four."