The Dark Blues needed to beat the Dons at Dens Park on Sunday but their 1-1 draw means they drop out of the top-flight after just one season.
Brown's men had looked to be on course for victory after Jim McAlister's deflected first-half strike and a straight red card for Reds striker Rory Fallon for an off-the-ball kick at Declan Gallagher had put them in command.
But their attempt at a remarkable escape act, which had already seen them twice postpone demotion by beating St Mirren and then Hearts, was finally snuffed out when Aberdeen midfielder Peter Pawlett took a tumble in the box to earn the visitors a 69th-minute penalty.
Niall McGinn rammed the spot-kick home but replays appeared to show that Pawlett had gone over easily as he was challenged by Lewis Toshney.
McInnes said: "It was not today that has cost Dundee. Bomber and his players can take a lot of pride from what they have done over the last few weeks.
"Dundee are in good hands, there is no question about that.
"When you see what Bomber and his players have put into it, there is a feeling of sympathy for that. But he's been in the game longer than me and knows what it will take to get back.
"After the game I shook his hands and just said 'unlucky'. I know how he will be hurting. There's not a lot you can say."
- Sports & Recreation
- Peter Pawlett
- Declan Gallagher