Rafa Benitez suffered his first defeat as Everton boss. Picture: ADRIAN DENNIS/AFP via Getty Images
Second-half goals from Matty Cash, Leon Bailey and a Lucas Digne own goal meant it was a miserable trip back to Merseyside for the visitors.
Moments before Cash broke the deadlock, Everton winger Demarai Gray flashed an effort just wide of the post. Full debutant Salomon Rondon and Alex Iwobi also spurned decent opportunities.
Benitez told the club's website: “We started the game quite well and in the first half had a lot of situations on the counter-attack where the final decision was not right – but we were very close.
“In the second half, we had a couple of chances, that could have meant everything was totally different.
“Then we conceded the goal and very soon conceded a second and it was difficult for us.
“Salomon, Demarai Gray and Alex Iwobi [had chances], so we had two or three situations where it could have been different.
“We made mistakes and we made them too early, too close, then it was difficult to react and that is something for the future, hopefully, we can manage.
“Either not concede, or if we do concede, react like we did in our games at home.
“The two goals were too close and then it was more difficult.”
Everton were depleted by four key players at Villa Park.
Dominic Calvert-Lewin was a known absentee heading into the encounter.
However, the Toffees were also without Richarlison, captain Seamus Coleman and Jordan Pickford.
The quartet will be absent for at least two weeks.
Benitez said: "At the moment we think it would be two to three weeks minimum [for Richarlison, Pickford and Coleman] and after we will see.
“[Jean-Philippe Gbamin] was a little bit tight in his quadriceps so as a precaution we decided to keep him out of the squad.”
Abdoulaye Doucoure felt it was always a challenge for Everton to get back into the game after Villa took the lead.
The midfielder said: “The result is a big disappointment for us because we were in a good moment,” Doucoure said.
“The team was doing well. We missed some key players, so it was hard for us. It is a small setback and next week we want to come back and win at home.
“I think we played quite well for 60 minutes.
“We had a great chance just before they scored, and I think the game could have been different but we know in the Premier League every game is tough. They scored one goal and kept the momentum, and it was hard for us to come back.
“We need to work hard and change this defeat into a win in the next game.”