Villa had exited the competition to lower-league opposition in four of the previous five seasons.
But Agbonlahor netted for the fourth successive match to earn Villa victory, although Cardiff boss Dave Jones felt his side had a perfectly good effort from Jay Bothroyd ruled out for offside in injury time.
O'Neill said: "I think that Cardiff were never out of it, and played some nice football, but we seemed to be in reasonable control, and I am delighted to have won and avoided another defeat in the competition.
"Agbonlahor is on fire at the moment, he is playing brilliantly for us. He has got so much confidence now.
"The goal he scored was maybe the sort he would not have attempted three-quarters of the way through last season, but he has so much confidence."
O'Neill was pleased with the performance of rookie midfielder Fabian Delph.
He said: "Fabian is going to be some player for us. He will become a proper player.
"I am pleased with the progress he has made since coming here, although I don't want to put too much pressure on him."
Villa have now chalked up six successive victories, and again were without the services of midfielder Nigel Reo-Coker after his training ground spat with O'Neill.
O'Neill said: "There is no update regarding Nigel. I have nothing more to add."
Jones felt that Bothroyd's goal in stoppage time should have been allowed.
He said: "I spoke to the referee, and I asked the linesman about it. I was well behaved, but I thought it was a goal.
"He was not offside. But I know I will get many decisions for me and many against me, and, because of the way we played, I am probably being a bit more diplomatic.
"I was very pleased with our performance, particularly after going a goal down after only three minutes.
"It was a big blow to us, but we recovered from that and passed the ball better than at the weekend, and overall everyone on my side did well."
Agbonlahor converted a low cross from John Carew after only three minutes to settle the issue.