Everton boss David Moyes has ruled himself out of replacing O'Neill, who 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.
Better times: Lerner with Martin O'Neill before the Northern Irishman walked out
Lerner admitted at the end of last season he would prefer a 'sell-to-buy' policy after backing O'Neill financially for the previous three summers.
But the American is adamant there has been no change in Villa's approach to building the club and being as competitive as possible.
HAVE YOUR SAY. Are Aston Villa better off without Martin O'Neill? Martin O'Neill has stunned Aston Villa by resigning in the week before the new Barclays Premier League season. But the Northern Irishman had indicated in April that his time at Villa Park might be coming to an end, so is a parting of the ways best for everyone in the West Midlands? TELL US WHAT YOU THINK Lerner insists the immediate priority is to resolve the Milner transfer and give support to caretaker manager Kevin MacDonald.
After coming under pressure to break his silence, he said in a statement: 'Having had some time to reflect on Martin leaving, I can say that our most immediate focus is supporting 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.
'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.'
Moyes has been touted as a successor to O'Neill, but the Everton boss insists he has no interest in the post.
Fans favourite: Ajax boss Martin Jol is the No 1 choice to succeed O'Neill at Villa
'I am loyal to Everton, I've always said that,' the Scot told talkSPORT. 'It is a really good club and this year we have a really good team and we have a good chance of doing well.'
All smiles: David Moyes is contentto stay at Everton
Ajax manager Martin Jol is Villa fans' No.1 choice to takeover according to a local newspaper poll.
Jol is wanted by 28 per cent of Villa supporters in a survey conducted by the Birmingham Mail.
The former Tottenham boss lookedset to move to Fulham last month before Ajax insisted he saw out the remainder of his contract.
Moyes is the second choice, polling 16.8 per cent, with Jurgen Klinsmann in third spot (12.1 per cent).
Birminghamboss Alex McLeish collected 3.5 per cent of the vote despite the rivalry between the clubs. But City are confident McLeish will commit his long-term future to St Andrew's by signing a new deal.
Sven-GoranEriksson has already indicated he would be willing to take over from O'Neill. Former skipper Gareth Southgate is also believed to be keen on the post.
Randy Lerner's right-hand man hits out at former Villa boss O'Neill Sign up to our FREE Fantasy Football game - with £40,000 in prize money up for grabsWill England star Young be first to follow quitting O'Neill out of Villa?You never gave me a chance! Villa outcast Davies blasts departed O'NeillASTON VILLA FC