The Hammers drew 2-2 with Newcastle on Sunday (05.07.20) to move four points clear of the drop zone and the boss believes his side must be prepared for the fight to go to the wire.
Speaking after the game, the former Manchester United coach said: "We came to Newcastle, who are in a decent run of form and in a good moment, so I'm really pleased that we've got something from the game. But I'm maybe a bit disappointed that we didn't get all three points.
"But I have to say the players are showing great fight and we're going to go right to the end. This league could easily go right to the last game of the season - we understand that and we're prepared for that if it has to be done.
"But we're trying to make sure that we can do it as quickly as possible."
West Ham led twice during the game and Moyes was frustrated to see Jonjo Shelvey earn a point for the Magpies in the second half, just seconds after Tomas Soucek had put his side back in front.
The 57-year-old manager said: "I was sickened, just because of us working so hard to get a goal back and then giving it up so quickly.
"We're in a group of games where we think we have got chances of picking up points. If you turned it around and we had got a point against Chelsea and three against Newcastle today, I think people would have said it was a great return."