Moyes, who was in charge of Sunderland when they finished bottom last season, told West Ham's website http://www.whufc.com that his current team can use their home form to avoid the drop.
"I'm not as anxious as I was when I first came in because we were in the bottom three then. The big job is to stay out of the bottom three and we've got three games to go," Moyes said.
"...I'm hoping we can turn those last two home games into points. We'll also go to Leicester next week, so if we can turn that or one of the two home games into a win, then I think we'll be OK.
"We've got Manchester United and Everton still to come here at home and I hope that somewhere along the line, seeing as we're in relatively good form at London Stadium, that we'll get the win we need."
West Ham travel to Leicester City in their final away league game on Saturday before hosting second-placed Manchester United and eighth-placed Everton at the London Stadium in their last two matches.
(Reporting by Aditi Prakash in Bengaluru; Editing by Christian Radnedge)
