It was the first time Rovers had won at Selhurst Park and O'Driscoll said: "In this league you have to not only perform, you have to do things like defend, and we did really well.
"I thought we were excellent. Palace are a difficult team to defend against and we took our chances well.
"In this division you need a little bit of luck and we took it. Regardless of the result, I told my players they were organised, our back four especially."
Palace should have been 2-0 up after half an hour but for two glaring misses from Neil Danns and Darren Ambrose.
Danns somehow managed to fire wide of an empty net from five yards out after Neil Sullivan had parried Victor Moses's shot into his path.
Then Ambrose tripped over the rebound from another Moses effort.
Palace manager Neil Warnock could not believe Danns' miss.
Warnock said: "I haven't got a clue how he missed that. I thought he had had a bet on the game, because there is no other way to explain it.
"It was a bad miss and it gets worse every time you look at it. And instead of going a goal up we lose by three, which could have been five. I've told him to come up and tell you how he missed it. I'm not sure he will though.
"We could have been 2-0 up by half-time. I am glad we have got Reading followed by Sheffield United up next. We do a lot better against the big teams."
Palace's players were told last week their November wages would be delayed until Tuesday at the earliest, due to chairman Simon Jordan's "cash-flow problem".
But Warnock denied this had anything to do with the performance against Rovers.
"I'd love to blame it on that, but that wasn't the case," he added.
Doncaster took a deserved lead four minutes before the break with a well-taken volley from Sharp.
Warnock must have made his feelings known because Palace came out firing in the second half and dominated for a brief spell.
Ambrose was denied by Sullivan's one-handed save a minute after the restart before a clutch of Doncaster defenders managed to clear Alan Lee's header off the line.
But Doncaster soon doubled their lead as Sharp set up Woods to blast home from just inside the box.
Hayter wrapped things up on 75 minutes by taking advantage of some shoddy Palace marking by rifling home from just inside the area.