The Toffees made light of off-field problems with a strong display only for Aston Villa to come from behind twice and preserve their unbeaten Barclays Premier League this season record with a 2-2 draw.
The game had been preceded by a peaceful protest outside the stadium by Everton fans frustrated at a lack of investment under chairman Bill Kenwright.
After two years without a significant transfer fee being paid, tensions have noticeably risen since last week's sale of star player Mikel Arteta.
Yet with Kenwright being applauded inside the ground, the majority of fans still appear to be onside and Moyes was pleased to give them something to cheer.
Moyes said: "Three or four of the players got at them, gave us a start and that got the crowd right behind us.
"It is a great place when the crowd is the way it was, it was terrific.
"I think the crowd responded to how well the players did in that opening period.
"You couldn't fault the attitude, effort and commitment the lads showed. I think the crowd picked up on that."
Everton completely dominated early on and claimed a deserved half-time lead through makeshift forward Leon Osman.
Villa rallied after the break and Stiliyan Petrov scored a sublime equaliser but they needed a late Gabriel Agbonlahor header to earn a point after a Leighton Baines penalty.
Moyes, whose side were also denied two good penalty appeals, said: "It was frustrating because our performance probably merited more.
"But we were playing against a good team - they have been in good form.
"We always knew it was going to be a tough game and in the past we have always had tight, exciting games against Villa. I think today was the same.
"Our play was exciting. We tried to score good goals and do the right things.
"Overall, we have not got many problems.
"I am disappointed with have lost two goals, one from 30 yards and the other from a cross, but I thought today's performance was really good and the players did a good job."
Villa boss Alex McLeish was pleased with the response of his team after a dismal opening period.
"We were a bit insipid in the first half," the former Birmingham manager said. "Everton dominated possession. We didn't really have too much to contend with in terms of the goalmouth but we never really posed a threat ourselves.
"It was a good chance to regroup at half-time and I am glad to say everything about the first half was the exact opposite in the second half.
"It is a good point. It is a hard place to come and it looks like they had a wee cause.
"We had to change it at half-time and the character of my squad came through."
New signing Jermaine Jenas, on a season-long loan from Tottenham, failed to make his debut after suffering a thigh injury.
McLeish said: "He got a kick in training and there was no way we would risk him.
"I think he was a bit over-zealous. He really pushed himself in training and he might even have felt it a couple of days ago but decided to train, such was his keenness.
"You can't knock a player for that and we hope it has not set him back too long and he will be with us in a couple of weeks."
Striker Emile Heskey left the action early after pulling a hamstring and will be assessed on Monday.