It was Andy Campbell who fluffed the 20th minute spot-kick when his shot was easily saved by Neil Sullivan.
In the second half Campbell, Cameron Jerome and Jobi McAnuff all hit the woodwork as The Bluebirds went in search of all three points.
The home side were without skipper Graham Kavanagh and fellow Irish international Alan Lee, who were both suspended.
There were the only two players in the City squad from their controversial 2-1 FA Cup win against Leeds back in January 2002, while The Whites had only Gary Kelly starting the match from that game.
City had claims for a penalty turned down as early as the 12th minute when it appeared Kelly had handled a Paul Parry cross, but referee Phil Crossley of Kent waved play on.
Four minutes later Sean Gregan was given a yellow card after cynically bringing down Gary O'Neil when the England Under-21 skipper was tearing down the middle.
After 20 minutes City had a glorious opportunity to open the scoring when a flowing move down the right saw McAnuff felled by Stephen Crainey in the area.
But Campbell's weak spot-kick was easily dealt with by Sullivan. His second spot-kick save of the season following the one at Wolves in August.
Leeds almost made the home side pay on the half hour when a Clarke Carlisle header from a Jermaine Wright corner was heading for the net, but Willie Boland managed a goal-line clearance.
On the resumption of the second half Brett Ormerod should have put the visitors ahead, but he screwed his shot wide with only Tony Warner to beat.
The Bluebirds hit back and Peter Thorne and Parry both had fleeting chances but the Leeds defence held firm with Carlisle a tower of strength at the back.
Kevin Blackwell brought on Julian Joachim and Michael Ricketts just after the hour in an attempt to open up the home defence, but the changes seemed to pep up Cardiff and Campbell hit the crossbar five minutes later with Sullivan beaten.
It was to be Campbell's last opportunity as he was replaced in the 70th minute by the 18-year-old Jerome, who was making his first-team debut.
Five minutes from time the youngster headed a Parry corner against the crossbar and then McAnuff struck a 20-yard shot on to the bar, but City were unable to clinch the win that would have sparked a disappointing season, thus far, into life.