For all their dominance, particularly in the second half, Celtic came up against a gritty defensive performance from the home side in which Rob Jones was outstanding.
Scott McDonald had the two best chances for the Hoops but overall they lacked any quality with their final ball to create clear cut chances.
Celtic boss Gordon Strachan had no complaints with his teams overall performance, only the fact they failed to score a goal.
He told :They showed great patience. It would have been easy with twenty minutes to go to throw long balls in, but we passed and we passed.
"We had chances, corner kicks, free kicks, incredible saves. We did everything apart from score a goal and that's the name of the game in football.
"I got some great performances today and I can't go into the dressing room and ball and shout at them.
"We have to win next week and hope Dundee United continue their good form against the Old Firm.
"If Rangers win then fair play to them. Well done."