The build-up to the game was dominated by Celtic's listless showing in the first leg and lack of recruitment throught the summer, but the side did little to right that wrong for much of the second leg.
The first half saw Kasper Schmeichel and the offside flag deny Kairat in their fleeting ventures forward, while James Forrest's header was smartly tipped over the bar. Both sides struggled to show any signs of attacking impetus as the first half, mercifully, drew to a close.
Rodgers opted to keep the same XI that started the game for the second period as he looked for a response from the players trusted to get the job done.
Despite reinforcements now seeming likely, the squad still looked uninspiring and without of a matchwinner as the riches of the Champions League hung in the balance.
As the tie slipped into the latter stages, a looping back pass from Callum McGregor had to be punched clear twice by Schmeichel, giving Kairat an indirect free-kick on the six-yard line.
It was blasted off of Maeda, with the hosts screaming for a penalty, but referee Maurizio Mariani waved away their spot-kick appeals.
Five minutes from full-time the best chance of the tie presented itself to Maeda as he raced on to the end of a well-weighted McGregor through-ball, but the forward couldn't compose himself and blazed over the bar. The hearty band of Celtic supporters that made the trip were disconsolate.
Kairat tired as extra time started but Celtic still remained unable to find any sort of effective route to goal.
A sharp intake of breath followed McCowan's saved shot as they continued to probe but failed to avoid the tension and lottery of a penalty shootout.
Idah stepped up first and had his effort saved, with Engels and McGregor the only two to convert on a grim night in Almaty.
