Dundee United manager Mixu Paatelainen is "desperate" to stay on and lead what he says will be a "massive fight" to get the club back to the Premiership.
The Tannadice club were condemned to the Championship following a 2-1 defeat to city rivals Dundee at Dens Park.
"This is a club close to my heart and I am more than motivated to do it, I am desperate to do it," Paatelainen said.
"We've got the knowledge of what needs doing with players and other issues. Only a fool would put that to waste."
Edward Ofere side-footed John Rankin's pass into the net to give Dundee United a second-half lead in a game they had to win.
But Kane Hemmings got a touch to Kosta Gadzhalov's header to nudge it over the line, and Craig Wighton found the far corner with a low shot in stoppage-time.
"It's simply not good enough, nowhere near good enough," said Paatelainen.
"Today, as on so many occasions, we had Dundee, we were comfortable, and then after that it's sheer softness, poor defending, not taking responsibility, not enough leadership, not ruthless enough.
"We are nowhere near the standard we should be.
"We've been here a few months now working with the boys. They're honest boys, they try hard, but we need to make so many changes. Not only team-wise but also elsewhere to bounce back stronger.
"There's so many slack areas in the football department, we simply need to improve those before we get better. We need to get a strong, hard working, hungry, energetic team out there."
Asked whether he believes he will still be manager next season, Paatelainen, who took over in October, admitted his future is uncertain.
"It's not in my hands," he said. "But I am desperate to build this team again."
Dundee manager Paul Hartley refused to gloat at United's demise, and instead praised his side and challenged them to continue to finish the season strongly.
"I'm really proud of my players," said Hartley. "They dug in, they showed a different side to them. We controlled the game. United played route one but we handled it really well.
"We've probably drawn too many games but we're a good team, we've got good players. They keep going to the end.
"It means Dundee are the only team in the city in the Premiership next season but I'm not here to celebrate Dundee United going down.
"It was important for us to win, we want to try and finish the season undefeated, stay seventh, we've beaten last year's points tally, financially it's important we finish as high as we can."