Pompey would normally be granted a place in Europe next season by virtue of having reached next month's FA Cup final against Chelsea.
But they did not apply for a UEFA club licence ahead of the March deadline for English teams to lodge paperwork.
The FA are now poring over the debt-ridden club's application, which could have significant consequences for O'Neill's side.
Should Pompey's bid fail, the side who finish in seventh position in the Premier League would qualify for the Europa League.
If they succeed in persuading the FA that their finances are in order, however, only the Premier League's top six sides will go into the competition.
Villa could drop into seventh if Liverpool beat West Ham on Monday night and O'Neill wants the situation resolved as soon as possible.
"Would I have a problem with Portsmouth's application to get into Europe? I probably would if we finished seventh, yeah," the Villa boss said after seeing his side beat Pompey 2-1 at Fratton Park.
"I don't know what the rules are. I didn't check them all. The only thing I ask for is that whatever the viewpoint is, the FA should resolve it before the end of the season to give those people chasing Europe the opportunity to know where they stand.
"If they haven't gone in for it in the first place, or applied for it themselves then you'd have to ask Portsmouth themselves if they should be given the right to appeal. That would be their right as a club. I just don't know the rules."
Goals from Nathan Delfouneso and John Carew saw O'Neill's side overcome a determined Pompey team who had taken the lead through Michael Brown's ninth-minute goal.
Delfouneso's winner came from his first touch after being introduced with little under 10 minutes left.
O'Neill admitted he thought Villa's chances of a win were over until the 19-year-old struck his first Premier League goal.
"I had thought during the second half that it wasn't going to be our day," said the Northern Irishman.
"When we were pressing there was always a chance of conceding at the other end, but we deserved to win and naturally I'm delighted.
"I'm very pleased for Nathan. He's an exceptional talent and I think given a bit of luck he can become a really good player for us."
Pompey manager Avram Grant had only 10 fit senior players to choose from, with Frederic Piquionne stranded in France following the birth of his third child.
The hosts looked tired towards the end of the second half and, had it not been for a superb performance from former Villa man David James, the away side could have bagged four goals.
The highlight of James' game was his first-half save which denied John Carew from the penalty spot.
Grant rates the 39-year-old as the best goalkeeper at Fabio Capello's disposal.
"For me it's nothing new. He's played so well all season," said the former Chelsea boss.
"He's had maybe one bad game, against Chelsea, but other than that he has played very good and for me he is the best English goalkeeper by far."
Grant also praised Pompey left-back Leonard Sowah, who became the first player who was born after the Premier League was established to start a top-flight game.
"He did great," Grant said of the 17-year-old.
"He played against a team with Ashley Young and Stewart Downing, who are very good players, and we are happy with him. It wasn't easy for him."