A foul on Billy Sharp gave Simon Cox the chance to level the scores inside the final 25 minutes and left Leicester boss Nigel Pearson to lash out at officials for a decision he thought was dreadful.
"I can see why the referee gave it, but in my view it was not a penalty," said O'Driscoll.
"I was tearing my hair out throughout the game and to be honest about it, we were lucky today. We have not got what we deserved in some of the games this season, but today we were fortunate to get a point.
"We got lucky and I hope it is another 20 games before we play like that again. We have played a lot better than that and come off losing matches.
"So we are thankful for the result but it is back to the drawing board as regards the performance. I don't think it was a penalty but I cannot go on the pitch saying, 'Don't give it me'.
"Referees are always going to make mistakes. It is part and parcel of the game. This is a difficult place to come at the best of times, and we did not perform today.
"But we got something out of it and have to make sure we learn lessons from it."