The Hammers head into this evening's Premier League clash with Stoke City in 15th place in the table, six points away from the dropzone, and the Scot is confident that will secure their top-flight future by avoiding defeat in their six remaining matches.
"It was a great point at Chelsea. It's not enough yet but the last two games have given us a lift," Moyes told reporters at his pre-match press conference.
"The ideal situation is to go unbeaten between now and the end of the season, there is no reason why we can't do that."
West Ham will go three games unbeaten if they avoid defeat against Stoke at the London Stadium.