Neil Mellor got Preston back on level terms three minutes before the interval before Sharp saw his 55th-minute spot-kick saved by Andy Lonergan.
O'Driscoll said: "We've had two away games in four days at Bristol City and Preston and we've got four points. I'd have taken that at the start of the week.
"Our goalkeeper has made a couple of saves in the second half where Preston have counter-attacked us.
"I'm disappointed because we had the chance with the penalty to get our noses in front again but this is a difficult division and if everything happened as you would want it to it wouldn't be so tight.
"Results like we had on Saturday (a 5-2 win at Bristol City) don't come along too often, but I thought with the way we played in the first half we could have been out of sight."
On Lonergan's stop, O'Driscoll added: "He made a fantastic save in the first half from Gareth Roberts as well, so he's earned his money.
"Billy will be disappointed with missing the penalty. Goalscorers want to score goals so he'll be a sulky boy on the way home. But he's been terrific for us. He's our top goalscorer, a bubbly character and he'll bounce back on Saturday I'm sure."
Opposite number Darren Ferguson felt his side should have claimed all three points after finishing the stronger.
"In the end we should have won it," he said. "In the last 10 minutes or so we had three outstanding chances.
Source: Team Talk