O'Neill is understood to have quit Villa after four years because he was not guaranteed all the money from the expected sale of James Milner to Manchester City to buy new players.
The Cleveland Browns owner, in a statement, said: "Having had some time to reflect on Martin leaving, I can say that our most immediate focus is supporting (caretaker manager) Kevin MacDonald and resolving the situation with Manchester City and James Milner. As for explaining why Martin left, I can say only that we no longer shared a common view as to how to move forward."
The statement continued: "To deal in greater detail would do little but cause additional distraction for the club as it faces imminent games and the clear priority of hiring a permanent manager.
"Finally, there have been no changes in our approach to building the club, aiming always to be as competitive as possible given our size and resources."
Alan Curbishley, reported to be among the favourites to replace O'Neill, has been backed as the ideal choice to manage Villa by Glynn Snodin.
Snodin was number two to Curbishley during his spell in charge at West Ham, and believes the 52-year-old would have a "massive interest" in taking charge at Villa where he enjoyed a spell as a player.
Snodin, who is currently number two with Northern Ireland and Leeds, said: "The Aston Villa job will be of massive interest to Alan Curbishley. He has been waiting for a top club and it is a top club, a big club.
"He's been there as a player and the experience he has got in the Premier League is massive.
"He gets his team organised and people say it's not exciting football but he gets teams like he did at Charlton and West Ham playing well and keeps them in the top 10 every year. What some of those clubs have done since then is unbelievable and maybe shows just how good a job he did do."
Source: PA
Source: PA