Roberto Martinez’s side dominated for long periods of the game but could not find a way past a resolute Cardiff defence.
Leighton Baines had strong claims for a penalty turned down in the first half, while Craig Bellamy wasted Cardiff’s best opening in the second half as both teams had to settle for a point apiece.
Everton created the first opening of the game on 12 minutes when Steven Pienaar’s clever flick set up Ross Barkley and the new England call-up saw his shot deflected just wide of the post.
Cardiff caused Manchester City all sorts of problems from corners last week and they went close to scoring after 16 minutes when Tim Howard just about clawed away Peter Whittingham’s in-swinging delivery at his near post.
Kevin Mirallas had a half chance on 24 minutes when he got on the end of Baines’ free-kick, but he could only loop his header over the crossbar.
Five minutes later Mirallas really should have broken the deadlock when some fine build-up play ended with Nikica Jelavic firing over a cross from the left, but the Belgium international failed to direct his header from eight yards on target.
Everton had strong claims for a penalty waved away four minutes before the break when Baines worked a one-two with Pienaar to charge into the box and he appeared to be caught by a sliding challenge from Gary Medel but, much to the surprise of the Everton players, referee Anthony Taylor waved play on.
Cardiff were indebted to goalkeeper David Marshall for going into the break all square after he produced a brilliant reflex save to keep out Jelavic’s header with the Scotland international showing great reactions to claw out the Everton’s striker’s deflected effort.
The impressive Barkley created an opening for Jelavic on 52 minutes when he slipped the striker in on goal, but the Croatian, who has scored just one Premier League goal in his last 25 games, lifted his shot well over the crossbar.
Things threatened to boil over three minutes later when Marouane Fellaini felled Fraizer Campbell 30 yards from goal and both players scuffled with each other, but the referee opted not to book either player.
Cardiff created their best chance of the game just past the hour mark when Kim Bo-kyung sent Bellamy clear on goal with a superb pass but, in rounding goalkeeper Howard, his touch was too heavy as it took him too wide of the unguarded net and the chance went begging.
Fellaini and Baines, who were the focus of all the attention before the game due to doubts over their futures, almost combined to score nine minutes from time when the former teed up the latter on the edge of the box and, with his weaker right foot, the full-back drilled his shot just wide of the target.
Substitute Gerard Deulofeu almost created a goal for Everton in the closing seconds when he fired over a dangerous ball right across the face of goal, but there was no one on hand in a blue shirt to get on the end of the cross.