"I write to Villa supporters to make clear that this relegation lies at my feet and no-one else's," he said in a statement on the club website (www.avfc.co.uk) on Friday.
"I know Villa will return better, stronger," added the businessman, who said the club's current plight was "totally unacceptable, unbearable and totally incompatible" with past glories.
"I will continue to try to put the club into worthy hands as I have, and also do my best to position Villa for the quickest possible return to its rightful place among England's elite."
Lerner, 54, bought Villa in 2006 but has been trying to sell the club since May 2014 without success.
Villa said this week, however, that chairman Steve Hollis was engaged in "extensive negotiations in relation to the sale of the Club."
The former European champions finished one place off relegation last season, despite reaching the FA Cup final, but this year's campaign has been one of abject failure.
The club, who have been in the Premier League since its inception in 1992, had their fate finally sealed when they lost 1-0 at Manchester United on April 16. It was their first relegation since 1987.
They have just three wins from 34 league games and have shipped 65 goals, more than any other club in the top flight.
Former Bank of England governor Mervyn King and ex-FA chairman David Bernstein both resigned as directors this week.
Villa are also looking for a new manager after parting company with Frenchman Remi Garde in March. First team coach Eric Black is currently in charge as caretaker.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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