If the dominant dismantling of a meek Dundee United side appeared to exorcise the demons of the brief Wilfried Nancy era at the weekend, this performance was a reminder of this Celtic side's fragility.
O'Neill was clear this week he feels signings are an absolute must, and being outplayed for most of the game by a side who were in the Championship this time last year will only turn up the heat on the club's hierarchy to urgently add quality.
The fact Nygren, a player who has gone from winger to midfielder and sometimes substitute, is the first player to hit double figures in the league this season - in January - is testament to their attacking struggles.
Luckily for Celtic the Swede has a fantastic ability to be in the right place at the right time, as he was again to get on the end of Arne Engels' dipping corner.
It was one of only two efforts on target as the champions toiled to build from the back, in large part due to Falkirk's ability to snuff out Callum McGregor's influence.
Nobody else stepped up to get them moving forward and they had little control.
McGlynn and Falkirk need to take immense credit for that, as they hounded Celtic and used their moments on the ball to play superb football.
Right-back Filip Lissah was outstanding, as was Leon McCann on the other side of the defence.
They were helped out at both ends of the pitch by wingers Calvin Miller and Wilson, who was only missing the finish from his excellent run in the first half.
The killer touch was all that was lacking. Still, they have a five-point cushion over Dundee United and Aberdeen in the race for the top six and deserve the be in the top half right now.
