Villa, who lost 3-0, were incensed that referee Howard Webb did not award a penalty when Gabriel Agbonlahor went down after a challenge by John Obi Mikel and that John Terry was not sent-off for his lunge on James Milner.
O'Neill, who had also spoken to Riley after the Carling Cup Final when Villa felt that Manchester United's Nemanja Vidic should have been sent-off, said: "I have spoken to Mike. He has shown some empathy and some sympathy with our frustration.
"But really at the end of it whatever he has said and what I have said should remain with the two of us.
"The game is past and the decisions have been made and you cannot change it.
"Overall, I must say that I am satisfied with the standard of refereeing and I don't think that there is much more to be said about.
"But we have had some really desperate decisions go against us at Wembley.
"People will sympathise with you on a Monday, agree with you on a Tuesday and say you are moaning on the Wednesday.
"It doesn't really matter any more. It doesn't change the result or change the course of history."
O'Neill has also confirmed that Milner has had a text message from Terry but added: "I have not gone into the details and neither was I concerned.
"I said at the time that it was a desperate challenge and it warranted a red card.
"I don't think anyone who has seen the replays will disagree with me.
"So I made my view clear at the time. It has gone and I am not worried
about any retribution."