Oldham dominated for large parts of the game, but it took a 77th-minute equaliser from James Dayton to earn a draw and keep City waiting for their first home league win of the season.
Jay Emmanuel-Thomas had volleyed City in front against the run of play after 36 minutes.
"I'm disappointed with our performance and Lee will feel his side did enough," O'Driscoll said.
"We never got any rhythm into our play and no one could have taken any pleasure from the display.
"We lacked quality and Oldham looked the more fluid team.
"We knew winning at Carlisle last week wouldn't mean a switch had been flicked and all was OK.
"But I expected better and by the second half I was just hoping for a scrappy victory.
"We still need that first clean sheet of the season desperately because you cannot hope to consistently out-score the opposition."