In a statement on the club's official website, Ashley said: "Seeing Newcastle United relegated from the Premier League has been a catastrophe for us all.
"I fully accept that mistakes were made during this and previous seasons and I am very sorry for that.
"I would like to say sorry to our magnificent supporters who have turned up in their thousands, home and away, up and down the country and who have given the team amazing backing throughout.
"And I would also say sorry to all of the club's hard-working staff, who have gone about their jobs all year long.
"Bringing Alan Shearer back to Newcastle United was the best decision I have made. Alan and his staff did all they could to try and keep us up in the short space of time they had.
"Talks are now ongoing between us about how we can take this club forward again."
Ashley, who took over in the North East in June 2007, was chastised by supporters earlier this season following the departure of Magpies favourite Kevin Keegan.
After heavy pressure, the businessman revealed he planned to sell the club, however, amid a difficult financial climate, he was unable to find a suitable buyer.
Ashley turned to Kinnear in September following Keegan's exit but the former Wimbledon boss was forced to undergo triple heart bypass surgery and Chris Hughton temporarily took the reins before Shearer was appointed.
SORRY NO CURE
whose the gal huh??
Pump 200 million pounds after we promoted
Originally posted by Y_Shun:whose the gal huh??
no idea, just thought it was better than pics of Ashley showing off his belly.
now then say sorry? for fcuk?
Originally posted by Y_Shun:whose the gal huh??
Thats what I thought too!
Newcastle United are the subject of fresh takeover talks.
Sky Sports says the investment bank representing Mike Ashley is in talks with an unnamed consortium regarding a possible takeover of Newcastle United.
Keith Harris, the chairman of Seymour Pierce, is believed to have travelled to the North East on Tuesday to hold talks with an anonymous group that is interested in buying the relegated Premier League club.