Jordan Rhodes put Rovers into a 34th-minute lead with a superb first-time shot from 20 yards out and they were in complete control during the first 45 minutes of the game.
And although the home side made a game of it in the second period, it still looked like Rovers would take all the points, up popped Robinson with an 89th minute leveller.
Black said after the game: "I'm bitterly disappointed.
"I thought Derby played exceptionally well and Nigel Clough had them motivated, but having controlled the game for a long period until 25 minutes to go I'm disappointed with how we responded.
"The goal came inevitably because of the possession they had and the crowd getting behind them. I don't think we managed that particularly well.
"We didn't get out to the ball, there was not enough pressure on the ball and we just dipped into trying to defend a lead. That came too early for me and that's what I'm disappointed about."