Derby battled back, Rob Hulse netting his 11th of the season with a neat finish, but the Rams' late charge amounted to nothing.
The result, Derby's fourth loss in five games, sends Nigel Clough's team down to 18th, while Doncaster extended their unbeaten run to four games.
Irrespective of Rovers' form, which puts them 11th in a tight Coca Cola Championship table, O'Driscoll said: "I don't really care where we are as long as we get enough points and we are in this division next season.
"I don't look at the table so I am not concerned.
"I keep saying to the players, 'if you want to win this division would you do anything differently? If there is why aren't you doing already?'
"My motivation is to stay in this division."
Whether his side pursue promotion or avoid relegation, O'Driscoll fears the state of the pitch at the Keepmoat Stadium could be decisive in the run-in.
"I think we did really well to cope with the pitch because at this minute in time it's not doing us any favours," he said. "I watched the England under-21s play here and they couldn't handle it so our lot did pretty well.
"We made hard work of it, but a lot of that is down to the surface. It will not help us play the way we want to play."
Derby boss Nigel Clough called on his players to "take more responsibility" after their poor away record continued.
The Rams have not won in their past five games on the road and have scored just 10 times away from Pride Park all season.
"We have looked nervous away from home," he said. "Not enough people grasping the nettle.
"(They are) always looking to someone else to do something. I want them to take responsibility for themselves and then to help their mates on the pitch.
"When it is not going well everyone retreats into themselves a little."
Clough was unhappy with the first-half penalty, awarded after Jake Buxton appeared to haul down Sharp, but he had no complaints about Emmanuel-Thomas' brilliant 69th-minute strike from 20 yards.
"We didn't play particularly well," he said. "We have been beaten by a dubious penalty and a wonder goal so we could have got something out of the game.
"The referee said he (Buxton) had a hand full of shirt. I would like to look back over his games this season to see if he has given a free-kick or penalty every time."
O'Driscoll was delighted with Emmanuel-Thomas, on loan from Arsenal, after his third goal in four games.
"I am very pleased with him," he said.
"He had an opportunity in the first half and he tried to chip it to Billy. We said at half-time if you get half a chance, pull the trigger.
"He has got a hammer of a left foot so we have been saying to him to have a shot when he gets half a chance.