As a result it was viewed as a missed opportunity against a team struggling for goals and seeking to avoid a fourth successive league defeat.
“It is not enough for us the point we achieved today,” said Emery.
“We conceded a few chances but we controlled the game and we created chances to win.
“In the last 20 minutes, even in added time, we never lost our mind and kept our game-plan in our mind.
“Now we have 41 points and are keeping more or less the the same position for the next couple of weeks (Villa do not play again until January 26) but we have to be focused on each match but also to improve what we can.”
Both goalkeepers were on top form, Jordan Pickford making good saves from Leon Bailey and Ollie Watkins, while Emiliano Martinez denied Dominic Calvert-Lewin in a one-on-one and also kept out James Garner.
Calvert-Lewin’s goalless run is now at 13 matches, dating back to October, but Sean Dyche insists it is only a matter of time before he ends his drought.
“I keep reminding him the further away it gets the closer it gets. One will go in,” said the Toffees boss.
“He did everything right, hit it hard and low and the keeper makes a good save.
“I hope he’s not worried about it. He’s working hard all the time, that’s what we want. We want clarity in the players’ thoughts.”
The match saw captain Seamus Coleman become the club’s leading Premier League appearance-maker with his 355th game and Dyche paid tribute, saying: “A fantastic servant, what he is and what he’s given to the side.
“It was a big day for him – deservedly so – and I’m pleased for him we got some kind of result as it would not have been an enjoyable moment for him.”
Dyche claims not to know anything about suggestions Everton could learn on Monday whether they will face any charges regarding profit and sustainability breaches relating to accounts submitted last month.
“Nothing at the moment, just waiting on the news. The last time (when they were deducted 10 points earlier in the season) the news came out of the blue.
“You don’t know until you know. I’ll explain further if and when the news comes through.”