Leighton Baines whipped in an early cross but Marouane Fellaini was unable to make any contact with the ball.
Kevin Mirallas then had a decent chance from a Baines free kick, but he headed over. The Belgian international was involved again, connecting with Nikica Jelavic's pass, but he failed to trouble David Marshall in the Cardiff goal.
Cardiff's Gary Medel brought down Baines in the box just before half time, but referee Anthony Taylor waved away the appeals for a penalty.
Jelavic then forced Marshall into strong save. The Croat was back in the action in the second half, flicking an effort wide of the post with the outside of his right foot.
Craig Bellamy had two good chances to put Cardiff in the lead, first with a free kick that Howard saved and then when he pushed the ball too far wide after rounding the Everton keeper.
Sylvain Distin had to be alert to clear the danger, before Mirallas went up the other end and found himself in space, only to be closed down by Whittingham.
Everton brought on Gerard Deulofeu and the youngster made an immediate impact, forcing Marshall to save. However, neither team could find the winning goal.