The Hammers travel to Manchester United tonight knowing that, despite Aston Villa's win over Arsenal, it would take an improbable 13-goal swing in goal difference, and results to go against them, to be relegated.
Moyes will not drop the party line that his side are still not mathematically safe but, having turned their form around, insists safety is not their only motivation to finish the season on a high.
"The maths tells you the job isn’t done yet so until the maths tells us different, we have got to prepare and make sure we are ready for the next game and take all three points if we can," said Moyes.
"The fact is that we haven’t changed. We are preparing ourselves as we have been, we are trying to become a more consistent side, we have been better not just because we needed to stay up but we want to get better in the future as well.
"Every opportunity you have to do that you need to try and take. I think going to Old Trafford is always a great experience for anybody and we want the players to go there, play well and show us what they can do."
Moyes has hit on a formula in recent weeks; West Ham winning their last two games and scoring seven goals in the process, conceding just once.
With that in mind, he is unlikely to make vast changes. The fitness of Ryan Fredericks remains uncertain, so would be a surprise to see anything other than the side which beat Watford on Friday take to the Old Trafford pitch.
West Ham predicted XI vs Manchester United (4-2-3-1): Fabianski; Johnson, Diop, Ogbonna, Cresswell; Rice, Soucek; Bowen, Noble, Fornals; Antonio