The Hoops' run of nine straight league titles seems certain to be ended by runaway leader Rangers as a point only edged Celtic to within 20 points of the top with two games in hand.
After defender Christopher Jullien tested positive on the club's return from the Middle East last weekend, the majority of the first team, plus manager Neil Lennon and his assistant John Kennedy, were forced to isolate.
A weakened team was also held 1-1 by Hibernian on Tuesday (AEDT) and any hope of catching Rangers faded away in a goalless draw which Livingston will feel it should have won.
Josh Mullin hit the bar for the visitors late on as their eight-game winning streak came to an end.
"It's not good enough," Celtic stand-in captain Callum McGregor said.
"It was really, really poor. It was a disappointing afternoon and we need to learn quickly. We're dropping too many points that's for sure."
While Australia star Tom Rogic was on the field for Celtic, the hosts did not have a senior striker available, and it showed as it rarely threatened the Livingston goal.
But 18-year-old Armstrong Okoflex nearly snatched all three points late on when he just failed to meet Anthony Ralston's low cross.
The sides meet again on Thursday (AEDT) when Celtic will have its first-team stars available.
However, their return is almost certainly too late to deny Steven Gerrard his first trophy as Rangers manager.
Elsewhere, Ross County's shock 4-1 win over Aberdeen lifted the Highlanders off the foot of the table as Oli Shaw scored twice.
Defeat for the Dons allowed Hibs to move up to third as it beat Kilmarnock 2-0 at Easter Road.
Hamilton remains a point off the bottom after a 0-0 draw against Dundee United, while St Johnstone beat St Mirren 1-0.
Motherwell is now bottom of the table ahead of a daunting trip to Rangers on Monday (AEDT).