"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."
The result maintains Everton's 100% start to the Premier League campaign, and moves Villa down to 19th place in the Premier League table.