They never looked like beating a Leicester City side struggling against relegation and could hardly string two passes together.
Stephen McPhail passed a late fitness test so the Bluebirds were unchanged from the side beaten at Sheffield Wednesday.
Ricky Scimeca was added to the bench which had its full complement of five players.
The visitors should have taken a fourth minute lead when a dreadful goal-kick by Peter Enckelman went straight to Dudley Campbell.
The striker raced towards goal but the Bluebirds keeper recovered to dive and grab the ball at the second attempt.
A close-range header by Steve Howard needed a fine reflex save from Enckelman as Leicester took control.
Enckelman was the busiest player on the field as he saved from Howard, Campbell and Iain Hume.
It needed a goal-line clearance by Roger Johnson to prevent Campbell from scoring in the 21st minute after he had pushed the ball beyond Enckelman and was bearing down on goal.
The visitors took the lead in the 27th minute when a clearance kick from keeper Paul Henderson flew down the centre of the field where Purse stuck out a foot to put the ball into the corner of his own net.
City had their backs to the wall for the last of the half and they were lucky to go in at the interval just the one goal down.
Steve Thompson replaced the unfit McPhail in the 56th minute but it made little difference as Leicester remained in complete control.
Cardiff were unable to raise their game in the final quarter and it was Ian Holloway's side who looked more likely to score as a poor game drew to a close.