Sunderland are the only team in the English top flight without a victory and are rooted to the foot of the table, with two points from their opening eight games. They are already four points adrift of safety.
"I spoke with a lot of supporters this week. I think they understand what's required. The bigger pressure is from you boys (the media). The supporters have been excellent," Moyes told reporters on Friday.
"There's pressure on every manager to get points, whether you're Sunderland or you're Pep at Man City. I've been at the other end, too – I know what it's like."
Sunderland visit 15th-placed West Ham United at the London Stadium on Saturday and Moyes has urged his players to be more ruthless.
"I think we've been really disappointed because we've been close in some games. We've had games where we've been in front and could have picked up points," said Moyes.
"Strangely, if you win one of those games it would look a lot different and we would be talking in a different way. But we've not and that's our fault. We need to cure that and get it better...
"One win would make a massive difference and it would lift confidence and get us much closer to the teams above us. It would give us a chance to start building."
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