Goals from Ashley Young and substitute Marlon Harewood pushed Villa closer to Champions League qualification and they are now level on points with their two main rivals for fourth place, Liverpool and Everton.
O'Neill said: "We were a threat all day, we looked capable of scoring and there was no question we deserved to win the game.
"Young was class. When Gabby rolled the ball across to him he still had to control it and when the goalie comes diving out he still has to put it past him. He took the goal brilliantly.
"Gabby was a handful and although he has done some light training this week that was nothing like a match so to see the game through was particularly pleasing.
"When Marlon came on he went wide right as he is capable of defending and that is the great thing about Agbonlahor and Young - they can drop into a position and if they pick it up from deep they are capable of going 30 or 40 yards with the ball.
"And Carew was immense. Playing like that, he is as good as there is. I have often said he doesn't realise how good he is. He had two decent opportunities early on - he knocked one across the box and blazed one over the bar - but John Carew now is full of self-confidence - as much as I believe he has ever had - and he was absolutely incredible."