Gael Clichy opened the scoring with an own goal before Gabriel Agbonlahor secured the win for Villa.
O’Neill told Sky Sports: “We have put in some really decent performances but, considering the opposition and our recent two losses, this was an incredible performance by us today.
“We have taken the game to Arsenal in the first half, considering how well they played against Manchester United last week.
“We were dominant and should have had the game out of sight at half-time. We missed a penalty and chances (to score). They were very strong mentally today.
“Today there was more than a great resilience about the side. We were absolutely majestic. We played wonderful football and deserved to win the game.”
He added: “There is a lot of hype. We have got a lot of work to do. That was an absolutely magnificent performance today but only that level on a regular basis will be enough.”
