Celtic found themselves behind at home when Livingston midfielder Jason Holt scored a 16th-minute penalty, but two goals in three minutes from Parkhead playmaker Callum McGregor and midfielder Ryan Christie had the Hoops ahead at the interval.
Albian Ajeti added a third in the second half to seal a comeback win for Neil Lennon’s men in the Scottish Premiership.
Livi defender Julian Serrano’s effort in the 78th minute ended up being in vain for the visitors as the league champions managed to hold on to a 3-2 victory and three valuable points.
However, Livingston boss Holt insists that Celtic’s second goal scored by Christie, set up with a smart cut-back by Greg Taylor, should have been disallowed as the left-back was in an offside position.
The Livi boss admitted that his side were defensively poor as they conceded soft goals that ultimately decided their fate, but thinks they did have Celtic worried when they pulled the score back to 3-2.
“I’m probably frustrated that we’ve come here played so well and conceded some soft goals”, Holt told BBC Scotland’s Sportsound.
“We threatened. When we get back to 3-2, we had them rattled.
“We got opportunities, we had chances.
“The second goal is offside for them.
“Taylor is offside.
“That’s the sticking one for us.
“That’s the decision that you need to go your way. It’s a sore one.”
Livingston are bottom of the Scottish Premiership table following the loss, while Celtic are level on points at the top of the pile with rivals Rangers.