Villa defeated Rapid Vienna 2-1 in the second leg of the qualifier but went out on the away goals rule after the tie ended 2-2 on aggregate.
O'Neill said: "We should have won. We did actually win the game. We should have got through. We should have had the game out of sight before they scored and it was unfortunate.
"They exerted some pressure at 2-0, which you would be expecting, but I thought we had a number of chances to go from 2-0 to 3-0 and that would have sealed the tie.
"Overall I was very pleased with the application of the side. I am desperately disappointed that we are not through.
"It would have been great experience again particularly for the younger players and last season, despite the way it ended for us in the UEFA Cup, I thought we had some splendid nights at Villa Park.
"I will miss those but we have to get on with it now and we will come again."
Ashley Young had a first-half penalty saved but James Milner converted another spot-kick and John Carew made it 2-0 before Vienna's late strike.
O'Neill said: "They were both penalties and the one time the ref did pretty well in the game was to allow the play to continue for the first penalty after Young was fouled.
"Ashley was disappointed to miss the penalty. He scored a great one against Liverpool and felt confident about taking it. James converted the second and then we went in front.
"We always felt we needed three goals in the game because there is the possibility of conceding. We had two good chances to seal the game.
"I thought the team played very well."
Vienna coach Peter Pacult said: "This is the nicest defeat we have ever had. A lot of uncomplimentary things have been written about me back home in the past few months and I hope I have proved a point with this result.
"I am also so proud for our fans. They were magnificent and deserved the result."