Under David Moyes this season, the Black Cats managed just five wins and a total of 21 points, scoring 26 goals and conceding 60.
They still have four games to play, against relegation-threatened sides Hull and Swansea, as well as Arsenal and leaders Chelsea.
In his statement, Short sympathised with the club's supporters while insisting plans were already in place for "significant" changes in the off-season.
He wrote on the club's official website: "Like any supporter, my initial reaction is one of sadness, disappointment, anger and frustration. After 10 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."