The Toffees go to Stamford Bridge sitting seventh on the Premier League table.
"I would have said it would be amazing, it was what I was probably dreaming and hoping we could probably do," Moyes admitted in his press conference on Friday.
"We have lots of data people around the place and I don't know whether they would see Chelsea being a point more than us, with the difference in the spend.
"But we are pleased. We are on a good run and we know it could easily change.
"We've won four out of five, but it could go the other way and it wouldn't necessarily mean that you are doing that badly, I just think the league is that tight.
"But if we want to keep ourselves in and around it we are going to have to keep picking up big results like we did at Old Trafford, like we did at Bournemouth, winning a home game against Nottingham Forest."