Dunne sat out training at Bodymoor Heath on Friday after travelling back from Paris - the scene of his country's heartbreak against France in the play-off second leg meeting.
O'Neill said: "Richard is very, very disappointed. He is pretty frustrated obviously with what happened and it is a real shame because Ireland were in a position to at least take the game to penalty kicks.
"It has been a devastating experience for Richard and I particularly feel for the experienced players in the side - the Dunnes, Givens, Duffs, Kilbanes and Keanes - more than the younger boys.
"It is a big blow to them. He didn't train today and I'm not surprised. He has had two very heavy games, particularly the match on Wednesday, and then you are hit by the major blow of not making it to the World Cup.
"Let me put it this way, he won't get over it overnight. I will sit down with him if we get an opportunity to see how he is feeling.
"Of course, disappointment can be overcome but I will speak to him and see how he feels (about playing tomorrow)".
O'Neill is looking for striker John Carew to maintain the form he showed two weeks ago when scoring once and setting up three goals in the 5-1 demolition of Bolton.
O'Neill believes that the Norway international is in the most consistent form of his career - but is still demanding more from Villa's leading scorer of the past two seasons.
He said: "It is all about consistency and I am asking for a pretty high level of consistency.
"John has a lot of talent and my own view is, he had an excellent opening spell in his career at Valencia but here has been his most consistent form.
"We are striving for more from him because he is capable of producing more. We are not asking for something he is not capable of producing. But with the form he showed against Bolton, he is priceless to us."
O'Neill also believes defender Luke Young has been premature in deciding to hang up his international boots with England.
Fabio Capello considered recalling Young for last week's friendly against Brazil but he reiterated his decision of several months ago not to want to be considered for his country again.
O'Neill said: "I was aware of Luke's decision a while back and it's always up to a player to make up his own mind regarding such matters.
"In my opinion, I believe it is a bit too early in Luke's career to be giving up things like that but I respect his decision."
Villa centre-back James Collins had been hoping to return against the Clarets after missing the win against Bolton with a groin problem.
But he suffered a reaction in training on Friday and is now regarded as a doubtful starter.
O'Neill said: "James was on the training field this morning and felt some discomfort towards the end. That was disappointing to hear and we will have to see how he is in the morning but I would say he is a doubt for the Burnley game."
Skipper Stiliyan Petrov and defender Habib Beye will both return after suspension and are included in the squad to face Owen Coyle's side.
Aston Villa 5/4, Burnley 9/4, Draw 9/4