After their 5-1 victory over Birmingham City, O'Neill said: "We have put ourselves in with a chance. I've a lot of time for Everton, and it has been a terrific season for them in the league and in a couple of cup competitions.
"We go there knowing we have to win the game, and the good thing is we have given ourselves a chance."
O'Neill believes the current goal power being shown by Villa has been on the cards for much of the season.
He said: "I think we have been creating chances all season. Now they are starting to fly in, and only Manchester United have scored more goals than us.
"Unfortunately, we also concede a lot of goals, maybe that is inevitable with the way we play, but we are attack minded."