Wade Elliott scored the only goal of the game at Ashton Gate to secure all three points for Lee Clark's men.
That was despite O'Driscoll feeling that his side started the game well.
"I thought we started really well, possibly too well," O'Driscoll told reporters.
"The gameplan went out the window and we played off the cuff. It coincided with us conceding in a silly 10 minutes.
"We've come away with a 1-0 defeat, which is possibly par for the season."
O'Driscoll said that plans are already in place to help secure the Robins' return to the Championship next season.
"We have a strategy as a club," he added. "It's talk at the moment though. We need to stick to that.
"We want to build a team that's lively to embark on the next challenge, which is to bounce back.
"We want to be positive. The fans stuck behind us. I've said about them in my programme notes. We thank them for their backing."
Relegation brings to an end City's six-year stay in the Championship.