Manager Ian McCall said: "We played well but just couldn't seem to get the ball in the net.
"We had the better of the chances, particularly in the second half we were unlucky when we hit the bar."
Queens started the brighter forcing three corners in quick succession. At the other end they had a lucky escaper when a sliced clearance left Steven Craig with a chance in front of goal, but he was unable to control the ball.
The best chance at that stage however, came to Queens just before the break when a long clearance from defence left sub Gary Wood with only the keeper to beat, but he fluffed his shot and the ball went wide.
Queens' luck was out midway through the second half when a neat interchange between Paul Burns and Eric Paton set up Stuart Lovell and his 18-yard drive crashed against the crossbar.
But seven minutes from time Queens keeper Colin Scott brought off a tremendous save when he touched an 18-yard drive round the post.
Dundee boss Alan Kernaghan said: "Both teams put up a good performance in conditions that were far from ideal and praise to the players for their efforts."