The Bairns paid for their profligacy when Celtic stole the points with the only goal of the game six minutes from time.
The average age of John Hughes' back four is around 20. But they had performed stoically throughout until a lapse of concentration allowed Shaun Maloney to find Aiden McGeady 25 yards out and the striker's right-foot shot arrowed just inside Scott Higgins' right-hand post.
It was cruel on a Falkirk side who outplayed the visitors for large parts of the game and indeed they might have gone ahead within 30 seconds of the kick-off. Patrick Cregg slipped Anthony Stokes clean through on the inside right position, but the on-loan Arsenal striker hit tamely at Artur Boruc when it looked easier to score.
Pedro Moutinho had a similar opportunity shortly after but again the finish was weak and when the same player cut back from the byline five minutes later, Cregg was unlucky to see his connection at the edge of the box blocked.
Celtic meanwhile were playing the ball around well enough but there didn't seem much point to it and the home goalkeeper was never in any danger of breaking sweat.
Celtic's left side, where Lee Naylor was often faced with a couple of players running at him, was a weak point and when Moutinho flashed past the left-back in the 28th minute the home side's lack of a strike force was underlined when Cregg pulled the striker's cut-back well wide.
Ten minutes before the break the home team ought to have broken the deadlock when Thomas Scobbie headed across goal to Darren Barr, but just when the youngster's header looked to be going in, Kenny Miller made a block with his chest on the line.
The visitors tried to inject some urgency into their play when Gorden Strachan pulled off Shunsuke Nakamura and the anonymous Thomas Gravesen and replaced them with Maloney and Evander Sno in the 59th minute. But there seem much difference to the pattern that had gone on before.
With 68 minutes played Falkirk again passed up another golden chance when the clean-through Stokes dithered with only the keeper to beat and Gary Caldwell got back to block.
Visiting keeper Boruc dived full length to turn an Alan Gow net-bound shot superbly round the post in the 78th minute, before McGeady pounced to steal all three points.