James Forrest struck wide for Celtic in the second half
Celtic and Rosenborg remain goalless after the first leg of their Champions League third qualifying round tie.
Vegar Eggen Hedenstad's free-kick tested Celtic goalkeeper Craig Gordon and Rosenborg's Yann-Erik de Lanlay fired over from close range.
James Forrest and Stuart Armstrong threatened for Celtic but they struggled to create openings.
And Gordon was called upon to make another save late on, denying substitute Matthias Vilhjalmsson.
The sides meet again in Trondheim next Wednesday to decide which team progresses to the play-off round, with the loser dropping into the Europa League play-off round.
Celtic were stymied by their lack of a central striker, Moussa Dembele out injured until September and Leigh Griffiths suspended and also carrying a knock.
Tom Rogic started in an advanced position in the absence of Dembele and Griffiths
As a consequence they lacked presence up front.They had, for an hour, midfielder Tom Rogic as a de facto front man but he never looked comfortable.In truth, none of Celtic's attacking players looked effective until late in the day.
They were denied space and chances by a smothering Rosenborg, who played deep and snuffed out Celtic's dangerous runners.Scott Sinclair barely got a kick.Fellow wide man Forrest looked hesitant for large parts of the night.
Brendan Rodgers' team had most of the ball but opportunities were thin on the ground.Forrest had a couple of weak shots blocked and then a header easily cleared.He should have had more of those moments.
In between, Milan Jevtovic and Anders Konradsen reminded their hosts that though they were living off scraps they still posed a threat.
What was massively frustrating for the vast and noisy home crowd was Celtic's inability not just to score but to trouble the Rosenborg goalkeeper.Andre Hansen did not have a save to make for the longest time.Indeed, when a save was required it was Gordon who made it, clawing away a rasping Hedenstad set piece.
Spectators would have expected Celtic to find themselves at some point but on the restart it was Rosenborg who made all the running.
Hedenstad had that free-kick, then the visitors carved out of a magnificent chance, passing their way through a confused home defence.When the ball came to De Lanlay he was at point-blank range.Celtic Park held its breath.De Lanlay scooped it over when he ought to have scored.An enormous let off for the hosts.
Former Arsenal striker Nicklas Bendtner led the Rosenborg attack
A minute later, Rosenborg broke free again and once more Celtic were in bother.Nicklas Bendtner's effort might have been poor - allowing Gordon to make a comfortable save - but it was another scary moment for Celtic.
Jonny Hayes came on for Olivier Ntcham at that point and Celtic got back on the front foot.Forrest fired one narrowly wide and just when it seemed like they might be building towards something they gave up another huge chance at the other end.
Mike Jensen created it and once more it was Bendtner on the end of it.Just as he did earlier, he made a hash of it.The big striker held his head in his hands in the aftermath.
He was not the only one.Most Celtic fans were doing exactly the same for entirely different reasons.
Incredibly, Celtic's first attempt on target came in the 77th minute when Armstrong forced a save from Hansen.
With time almost up, Rosenborg had another massive chance when De Lanlay's replacement Vilhjalmsson almost beat Gordon from close range only for the goalkeeper to kick away his effort.Another gobsmacking episode for the home support.
A goalless draw ahead of next week's trip to the Lerkendal Stadion was more than they deserved.
Rodgers will be praying that Griffiths makes it.It's painfully early in Celtic's season, but they have already arrived at a pivotal moment....