The Hammers are above the bottom three only on goal difference ahead of Wednesday night's match against Chelsea at the London Stadium, having suffered back-to-back defeats since the restart.
Moyes said: “If somebody asked me now where I thought we were going to finish, I'd say you'll probably have to wait until the last day of the season to see how it goes.
“I had a similar position the last time I was here. But I see this one as a much tougher fight at the bottom of the league than I did at that time.
“Are we pleased we're not in the bottom three? Of course we are. But we know that unless we win, we will be. It's down to us to win."