"We're the ones who are chasing the pack, we have to try and catch the others up," Moyes told Sky Sports as the bottom side lost their third consecutive league game.
"The players have had the experience of surviving before, so hopefully we can. Nobody in the dressing room is saying we're gone. We're far from it.
"We will stick at it, keep doing what we are doing and it will turn. We have to just hope our fortune changes in the coming weeks."
Moyes will see his survival hopes boosted by the return of key players from long-term injuries, including defender Lee Cattermole (hip injury), midfielder Jan Kirchhoff (knee injury) and striker Victor Anichebe (knee injury).
(Reporting by Aditi Prakash in Bengaluru)
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