Ahead of Saturday's visit of Burnley, Moyes is expecting a reaction from his players after consecutive 4-1 defeats at Liverpool and Swansea City.
"We have had good results at our stadium and we have got to make that count," he told a news conference on Friday.
"We have six games remaining at home this season and we think that in those six games we can accumulate enough points to stay in the Premier League.
"Tomorrow (against Burnley) is the first of them. The players know exactly what is required and what we need to do."
West Ham are 14th in the standings, only three points above the drop zone, and Moyes expects the battle for top-flight survival to go down to the wire.
"It is changing all the time because I don't think there is a lot between the teams from 10th down to the bottom," he added. "I think 40 points has always tended to be the safe bet. If you get 40 you are pretty much there. We have 10 points to go."
Moyes confirmed that defender Winston Reid has been ruled out for the rest of the season with a knee problem, while Sam Byram faces an extended spell on the sidelines with an ankle injury.
Italian centre back Angelo Ogbonna has recovered from illness, while defensive colleague James Collins faces a late fitness test on the hamstring injury that kept him out against Swansea last weekend.
(Reporting by Hardik Vyas in Bengaluru; Editing by David Goodman)
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