The Robins are in great form of late having won three of their last four matches and are now just three points adrift of safety in the Championship.
"We have two of the hardest away games possible coming up. I'm ever the realist and they don't come much tougher than Cardiff City and Crystal Palace away," O'Driscoll told reporters.
"We're playing two of the best teams in the division on their own patch; we need to prepare for that."
O'Driscoll's side are currently 23rd in the Championship on 31 points having played 31 games this season.