The owner says he takes full responsibility for the club's problems.
However, he did not clarify whether Paatelainen would stay on.
"In the near future many radical changes will be made to try to ensure our quick return to the top league," a United statement read.
Relegation from the top flight was confirmed after a 2-1 defeat by city rivals Dundee on Monday.
Thompson has promised sweeping changes to ensure an immediate return to the Premiership.
"Dundee United have let you, the supporters, down this season," his statement continued.
"I apologise unreservedly to all of you for our relegation. As the chairman the buck stops with me and I accept full responsibility for what has happened. The big decisions were mine and I got some of them wrong.
"I have backed managers with the third biggest budget in the league but the results have not been acceptable.
"Further changes will see increased fan representation as well as boardroom changes to revitalise and re-energise the club."
Former Finland boss Paatelainen, 49, replaced Jackie McNamara in mid-October, signing a two-and-a-half year contract.
United were bottom of the table at the time of his arrival, having picked up one win in their first 10 Premiership outings.
But Paatelainen, who had spells in charge at Hibernian and Kilmarnock, has overseen just five wins from 25 league matches.
Stephen Thompson has apologised "unreservedly" to Dundee United fans following relegation to the Championship, but manager Mixu Paatelainen's future remains unclear.