Saturday's 1-0 defeat by Bournemouth at the Stadium of Light ended the Black Cats' 10-year stay in the top flight a day after their latest financial figures revealed they had made a loss of Â£33million during the year to July 31, 2016.
American businessman Short, whose continued backing is keeping a business with a net debt of Â£110.4million afloat, promised to address the failings of recent years in a bid to reverse its fortunes on and off the pitch.
He said: "Like any supporter, my initial reaction is one of sadness, disappointment, anger and frustration
After10 consecutive seasons as a top-flight club, the second longest in our 138-year history, it is hard for everyone to take.
"It is an especially cruel blow for our supporters, who have shown tremendous faith in the club
They backed the team, home and away, in huge numbers throughout the season and it is fair to say this season they have once again been relentless in their support
I am truly sorry that we have not been able to retain our top-flight status for them.
"I acknowledge that during my ownership mistakes have been made, particularly in the area of player recruitment, and as a result we have found ourselves struggling to survive in recent seasons.
"We had massive disruption during the summer transfer window and an unprecedented number of injuries throughout the season
These are difficulties which we have been unable to overcome and we are paying the price for that now.
"We need to improve, both on and off the field, and despite the bitter disappointment of today, there is a strong determination to do so throughout the club.
"There is significant work to be done over the summer and when the season is concluded, we intend to share our plans to move forward with our supporters."
Manager David Moyes had earlier spoken of his sorrow at being unable to retain the club's Premier League status, but declined to talk about his own future.
Source : PA