The victory means the Robins have moved off the bottom of the table, and O'Driscoll believes City now have a fighting chance of survival.
"Credit to Barnsley because they certainly didn't come to shut up shop," O'Driscoll said. "They had a lot of chances, but so did we and it made for an exciting game.
"I said after our defeats at Cardiff and Crystal Palace that the spirit had not been knocked out of us and this display proved it.
"We still have a long way to go, but if the players can maintain that level of commitment we will give ourselves a chance.
"Our home form is good and we have improved in away games without getting any reward as yet."