Chris Cohen and Garath McCleary had good chances to score, with Mark Wilson going close at the other end, but Forest's poor run goes on at one of the most crucial times of the season.
Doncaster started on the front foot, with James Hayter's confident midfield play creating numerous early chances.
After 12 minutes, Franck Moussa tried his luck with a shot from distance which whizzed over the crossbar, and five minutes later Wilson attempted a copycat strike which went much closer to testing Lee Camp.
The hosts first showed their promise with 18 minutes played when Chris Gunter made a positive run down the right wing to supply a good cross into the box but there were no takers.
Two minutes later, Wilson was on hand to demonstrate great technique and blast a left-footed shot towards goal, the ball failing to dip in time and sailing over the crossbar.
In a spell of sustained pressure from the home team, Cohen was unlucky not to break the deadlock, his swerving drive being blocked by Shelton Martis, while Paul McKenna should have done better from outside the box, not testing Gary Woods in the Doncaster goal as his shot bobbled wide.
Woods was called into action for the first time after 34 minutes, having to parry a stinging shot from Radoslaw Majeski. Former Sheffield Wednesday striker Marcus Tudgay tried an identical strike six minutes later but his effort lacked accuracy and went wide.
The hosts were unlucky not to go in at the break ahead when Woods produced a brilliant save to keep Robert Earnshaw's sweetly-struck volley out.
Billy Davies' side rallied to subdue the organised Rovers and were given a boost when defender Martis was forced out of action through injury in the 54th minute.
Luke Chambers then drew a strong block from George Friend as Forest began to gain in confidence with the hour-mark approaching.
On-loan Kris Boyd was introduced as the hosts turned up the heat in their search for a victory, but perhaps to the surprise of the supporters, Tudgay was replaced by Lewis McGugan with 20 minutes remaining despite being key to much of Forest's attacking play.
McCleary had arguably the best chance of the afternoon to end the stalemate, receiving the ball in a good position in the box, but he lingered in possession for just too long before tamely clipping the ball towards Friend to the dismay of his Forest team-mates as the final whistle approached.