Just 32 seconds into the second half referee Robert Madley made the game-changing decision to dismiss Blackstock for an apparent elbow on Rams captain Richard Keogh.
"It came so quickly and there are aerial challenges all the time in the English game so I didn't know what it was for. That's the difficulty, when you don't know what it's for," O'Driscoll said.
"But, watching it on the replay, then I suppose you can see, to give the referee the benefit of the doubt, you can see why he gave it. But in the context of the game I just think it's a harsh one, very harsh."
The visitors made their numerical advantage count with Craig Bryson scoring the only goal of the game as Derby notched their third straight win over their great rivals, the first time they have put together such a sequence in 100 years.
While O'Driscoll stopped short of criticising Madley, he questioned his decision to give Blackstock his marching orders for what appeared an innocuous aerial challenge, particularly after more severe incidents went unpunished in the first half.
He added: "We'll have to look at it - see if we can get it rescinded."
If O'Driscoll was perplexed at the contest's turning point, Derby first-team coach John Metgod attempted to offer some logic to Madley's controversial call.
"I'm in the lucky position to go home and in about two-to-three hours' time, I'll have another look at it and make up my mind, which for the referee, obviously he can't," he said.
"The only thing I would say is I can't see a referee taking a decision like that if he's not absolutely convinced. If there was any doubt whatsoever, I can't see him sending him off."