Carter-Vickers error hands Falkirk an early lead
Celtic paid the price for a sloppy start as Falkirk struck in the third minute at the Falkirk Stadium. The visitors' central defence failed to deal with a long ball, and the hosts worked it out to Ryan Strain, whose cross was knocked into the path of Ethan Ross by Carter-Vickers.
The wide player lapped up the chance, but the goal came at a cost as Strain injured himself while crossing. Jack McMillan came on as a natural replacement at right-back, with Carter-Vickers back from injury and Alex Oxlade-Chamberlain handed his first start in two months.
Scott Bain frustrates his former club
On-loan Derby winger Owen Eames was a hive of creativity on Falkirk's left and set up two half-chances for Jacob Murrell, who could not make the most of them. The 19-year-old then created the second goal in the 38th minute, as left-back Scott Tanser ran on to his infield pass before slotting past Sam Johnstone.
At the other end, Bain made 10 saves in total, according to the Daily Mail. Camilo Duran hit a post after getting in behind, while the former Celtic goalkeeper denied the Colombian three times and foiled Haissem Hassan with a diving save.
VAR rules out Murrell goal as Celtic toil
Falkirk were almost out of sight early in the second half when Murrell bundled the ball over the line after Celtic failed to deal with a long throw. However, the ball had hit the American's hand as it bounced off a post, and VAR disallowed the goal.
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O'Neill brought on James Forrest at half-time before turning to Kasper Hogh and Benjamin Nygren, but Callum McGregor, Kieran Tierney and Hassan all missed the target from inside the box. Bain's brilliant double save from Forrest and Nygren then sparked chants of "Scotland's number one" from the home fans.
What next for O'Neill and Celtic?
Celtic remain four points clear at the top of the Premiership, but they have now played a game more than second-placed Rangers.
O'Neill must find answers quickly, with Hogh now 14 games without a goal, while Falkirk move up to fourth and will look to extend their winning run.