Fraizer Campbell's opener, a smart finish from Tommy Smith's clever through ball, broke the resistance of a stubborn Robins side in first half added time.
Campbell then secured the points from inside the box after being found by Aron Gunnarsson's huge throw.
The Robins did grab a consolation in added time when Ben Nugent scored a bizarre own goal, heading the ball past David Marshall under no pressure, but they were left to reflect on a third straight away defeat since the former Nottingham Forest boss took charge.
It was Campbell's second goal, a close-range finish from a long throw, which was especially frustrating for O'Driscoll.
"If we hadn't conceded a poor second goal we could have walked away with a point which would have been extremely pleasing," he said.
"The second goal was disappointing because every day in training we say we can't concede poor goals in this division. We didn't deal with that as well as we should have.
"They are a good team and with the front two of Campbell and [Craig] Bellamy they deserve to be a good team. Their movement and interchanging caused us problems.
"But credit to the lads they stuck in and stuck together and everyone has reacted positively to any negatives in the game.
"We've just got to be a little bit better with the ball. If you are going to win games away from home with limited possession then you do have to be effective."