A 25-yard rocket from Jay Emmanuel-Thomas got City off the hook after a lethargic first-half display which saw the visitors deservedly lead through a 28th-minute goal from Jon Taylor.
The home side were poor for the opening 45 minutes, failing to create a single chance, but they improved markedly to have the better of the second half.
Taylor's goal was a smash and grab raid out of defence as Luke Summerfield fed Curtis Main down the right and his low cross created a simple finish from eight yards.
It took a terrific right-footed strike from Emmanuel-Thomas to reward City's second half improvement, but O'Driscoll's men are still left without a League One win following relegation last season.
The head coach said: "We made a lot of wrong decisions in the first half, playing the ball short when it should have gone long and vice versa.
"When we went long it was because there was no alternative, rather than because it was the right thing to do. We were being dictated to, rather than being in control.
"At half-time, we offered the players a simple solution to what was going wrong and to be fair they responded.
"I have absolutely no fault to find with the effort and commitment and to an extent the lads are doing what is being asked of them, but we need to make more good decisions than was the case for 45 minutes."