Steven Pienaar handed the Toffees a third-minute lead with a stunning 20-yard strike, before Marouane Fellaini scored his second goal of the season, aided by Shay Given’s mistake mid-way through the first half.
Nikica Jelavić completed a dominant 45-minute opening period for the visitors, with the Croatian finishing from close range.
And Villa’s miserable afternoon was compounded when Ciaran Clarke was dismissed for a foul on the Everton striker in the second half. Karim El Ahmadi grabbed a consolation for the home side in the 74th minute.
“I know it’s a huge job here. We are trying everything to sort it out. For every negative there’s a positive and at least we didn’t capitulate,” Lambert told BBC Sport.
“Will there be any new signings? We’ll have to wait and see what happens over the next few days. It’s a really young side and sometimes you need a bit of help.”
David Moyes’ side have now secured back-to-back wins following their victory over Manchester United last Monday – and the Toffees manager was pleased with his side’s start to the season.
“We created quite a few chances before we scored and I was beginning to worry. I’m a bit disappointed we didn’t score one or two more,” said Moyes.
“I’d like to add to the squad if I could because it is a bit light. But if your squad’s light then it gives the youngsters a chance and we are a club that gives youngsters a chance.
“Six points from two games is a good start, particularly when your first two games are Manchester United and Aston Villa away.”
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