Police horses had to be brought on to clear the playing area after celebrating City fans ran on to goad the Rovers supporters behind one of the goals while missiles were hurled in both directions.
Jay Emmanuel-Thomas rocketed the Robins into a deserved lead with a fantastic left-footed strike from 25 yards in the 12th minute and the hosts could have been more than a goal up at the break.
Rovers were far more competitive in the second half and equalised when Mark McCrystal headed home a 59th minute free kick from Lee Brown.
But 19-year-old midfielder Joe Bryan curled home an exquisite winner for City with his right foot, the Bristolian's first goal in senior football.
O'Driscoll said: "The scenes at the final whistle have taken a lot of the gloss off our win. My players behaved as I wanted them to. Unfortunately, our supporters didn't.
"That will make the headlines and it's a shame because the match was competitive without ever going over the edge. Both teams approached it in the right way and I was delighted with how we played.
"I actually have seen Jay Emmanuel-Thomas score a better goal than that, but it was a brilliant strike that showed the lad's quality.
"Joe Bryan scored with his right foot, which is probably a first. I'm disappointed we gave away a few too many free kicks and conceded from one of them, but we responded well and I would be very happy, but for the disgraceful scenes at the end."