Leeds were leading through an 11th-minute goal from Paul Green when Sharp went down under challenge from Tom Lees to give the striker the chance to equalise from the spot.
O'Driscoll said: "We all know there are players throughout football who are likely to go down easily for penalties but Billy is not one of them. I don't think anyone in their right mind would say that Billy Sharp is a diver.
"What he does do is score goals. He's made his name doing that and if you give him chances he puts them away.
"He had a bit of pressure with the penalty in front of the Leeds fans because it was an important moment in the match.
"But he showed his quality when he was one on one against the keeper to score his second. Like one or two of the other lads he was a bit under the weather before the game but the two goals will not do him any harm."
The penalty proved the game-changer and Forest ripped Leeds apart with three goals in quick succession, starting in the 54th minute.
Sharp scored his second when Dexter Blackstock nodded down Elliott Ward's ball forward, rounding Paddy Kenny before shooting home.
Then Ward knocked a corner by Andy Reid back into the danger zone and Leeds midfielder Rodolph Austin could only turn the ball over his own goalline.
Four minutes later Reid found space for a left wing cross that Blackstock headed back across goal and beyond Kenny before David Somma pulled one back for Leeds.
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