The Toffees dominated a side who are chasing Champions League qualification and deserved a victory gained through goals from Steven Pienaar and Denis Stracqualursi
Loanee Steven Pienaar's early strike gave the Toffees the lead before the tireless Denis Stracqualursi grabbed a deserved goal to wrap it up.
And Moyes claims that Everton can kick on from this result, believing they impressed in all aspects of the game.
He told reporters: "That was a great result for us and good parts of the performance as well. The strange thing is I think we can play a lot better.
"I think we’ll play better once we get a bit of confidence and the wins take us along. A great result to beat Chelsea, we got off to a great start with the early goal and it gave us something to hang on to.
"We started well the first 15 minutes or so but I thought they grew into the game. We had to ride our luck a bit on a couple of occasions but I thought the second half we didn’t look as if we were going to concede. We defended brilliantly well.
The Scot also had words of praise for goalscorer Pienaar, who he says is suited to playing on Merseyside after a struggle for first-team football with Tottenham.
"You’d have come here and clapped him today," he continued.
"That’s why he did get clapped by everybody at the end. There were bits of his stuff that were terrific.
"I just said to him the dressing room it’s as if he’s never been away and maybe sometimes clubs fit players and that is the case.
"Maybe this just suits him. If he’s got someone who knows how to give him the ball at the right time, the right moment, and knows how to support him when he needs to release it. That’s why he was wanted by so many clubs a year ago."
The 48-year-old went on to disagree with opposite number Andre Villas-Boas, after the Chelsea boss suggested that he would not change his system to suit his players.
He added: "I think wherever you come you’ve got to work with the players you’ve got. You have to try and find a solution.
"I have to try and find the winning formula and I’ve been trying to do here for six months at the start of the season.
"[Some of our players] are only on loan and we know that, Landon goes away next week but it’s been a bit like that at Everton.
"We’ve not had great financial resources and we’ve tried to do what we can and wheel and deal around the loan market to see if it can get us a few results.
"If Landon can get us a few results, Steven Pienaar till the end of the season helps us get a few results then hopefully in time we’ll bring our own players through our youth academy or through signing them.
Finally, Moyes hailed Stracqualursi, claiming his goal was a reward for his hard work in training since joining Everton.
"It was fantastic. I think he’s got better," he said.
"He’s old-fashioned, when I played there were lots of that type of centre-forward about. Little bit huff and puff at times and not pleasing to the eye but by the end he wore them down. He’s got an iron lung and can keep going.
"He trains every day, he does extra every day, he’s never once questioned it and he’s determined to make a go of being successful in England. He deserves everything he gets."