The Dark Blues needed to beat the Dons at Dens Park but Niall McGinn's 69th-minute spot-kick cancelled out Jim McAlister's first-half strike and saw Brown's side sink after just one season.
Brown was furious after the final whistle and accused Peter Pawlett of diving to win the penalty but McInnes refused to be drawn on refereeing decisions, instead backing his old colleague to lead the club back to the top tier.
"It was not today that has cost Dundee," McInnes said.
"Bomber (Brown) 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."