Andriy Yarmolenko’s 89th-minute winner lifted West Ham to a 3-2 victory at the London Stadium on Wednesday.
Moyes’ side climbed into 16th in the table, three points clear of Aston Villa and Bournemouth.
But the Scot is hoping to see West Ham collect 10 points from their final six league games to ensure safety.
“If you get to 40 you will be safe in the Premier League so we have to aim for that tally,” manager Moyes told Sky Sports.
“It probably means winning another three games.”
You love to see it pic.twitter.com/YycSaLQCvY
— West Ham United (@WestHam) July 1, 2020
After Tomas Soucek cancelled out Willian’s penalty, West Ham led through Michail Antonio, only for the Brazilian to bring Chelsea level before Yarmolenko’s winner.
West Ham had earlier had a Soucek goal ruled out by the VAR with Antonio offside and Moyes lamented another decision going against his side.
“This VAR stuff I am beginning to lose faith with it. I was spewing. I was thinking are we going to get a decision here?” he said.
“I feel some of the things that have gone against West Ham recently has been really poor but I said to the players we had to change our luck.
“The players deserve a massive amount of credit. They are sticking to it.”
West Ham are away to Newcastle United on Sunday.
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