The Scottish champions had the chance to extend their lead at the top of the table to seven points, but never recovered from conceding a third-minute opener to Ethan Ross.
Scott Tanser slammed in a second before half-time and the Bairns even had a third goal ruled out by a VAR review for handball against Jacob Murrell.
The majority of Celtic's struggles this season have come in European competition as they crashed out the Champions League qualifiers and have lost all three Europa League group matches.
But sloppy defensive errors and a lack of a clear tactical plan is beginning to cost them domestically as well.
Rangers could now close to within one point of their Old Firm rivals should they win a game in hand.
"We're still in a decent position at this minute," said a defiant O'Neill. "I keep out the noise at the end of it all.
"A tough one to take because I know we conceded two goals but we could have scored six or seven dead easily."
Falkirk had not beaten Celtic since March 2007, but were well worthy of a fourth consecutive victory to move up to fourth in the table.
O'Neill recalled Cameron Carter-Vickers to the heart of his defence, but that decision backfired when the American international presented the ball to Ross to slam home the opening goal.
Former Celtic goalkeeper Scott Bain was inspired in the Falkirk goal to deny Haissem Hassan and Camilo Duran, while the later also struck the post as the visitors pressed for an equaliser.
But Celtic's leaky defence was exposed once more on 38 minutes when Tanser raced forward from left-back and drilled low into the corner.
Murrell thought he had added a third early in the second period, but was penalised for the ball brushing his hand before crossing the line.
At the other end Bain continued to perform heroics, denying substitutes James Forrest and Benjamin Nygren.
O'Neill, 74, twice rode to Celtic's rescue last season to take interim charge, 20 years after his first spell at the club ended.
The Northern Irishman then signed a one-year deal in June.
Yet murmurs of discontent among the club's fanbase have increased in recent weeks with many now calling for a change.
"I've managed this team now for about a year, give or take a month or two, and I've managed before," added O'Neill.
"We're still top of the league.
"We came from a mile behind last year to win the league. A mile behind on two or three occasions as well too."