City remain bottom of the Championship and three points adrift of safety, but O'Driscoll insists their recent performances have given them the belief to beat the drop.
"The players gave everything and no one would have known which team were bottom and which battling for promotion," he said.
"We have now kept successive clean sheets in goalless games with good sides. That is a big change from earlier in the season and the players have taken on board what I have asked of them.
"We now need that bit of extra quality, but if we keep on showing that level of commitment we will have a chance of surviving in the Championship.
"Perhaps I could have introduced my attacking substitutes a bit earlier, but we are not the finished article by any means and didn't want to lose the game 1-0 after such a big effort by the players."