Giorgios Giakoumakis netted a 95th-minute winner for Celtic in a dramatic finale to clinch a 2-1 win for the Scottish Premiership champions at St Johnstone.
The much-changed Hoops look set to drop points for the second time in three league games when defender Alex Mitchell slotted in an equaliser for the hosts in the third minute of added time.
But Giakoumakis turned home Alexandro Bernabei’s cross with virtually the last kick of the game.
“It’s a game we probably should have put to bed a little bit earlier with the chances we had,” Postecoglou said post-game.
“At 1-0 you know that it’s always on a bit of a knife-edge, particularly as they’re a team who will lump balls into the box, and you are going to have to defend sometimes pretty desperately.
“They obviously got the goal late, but again, there was great character and resilience by the lads. We did it a few times last year and we’re going to have to show that at times again this year.
“You can win a game of football in many ways, but I think winning it this way also provides us confidence in the fact that we still have that sort of resilience within the group.”
Celtic were beginning an extended spell without captain Callum McGregor after the midfielder suffered a knee injury in the midweek Champions League defeat by RB Leipzig.
McGregor was suspended for the trip to Perth, but manager Ange Postecoglou confirmed ahead of kick-off that the Scotland international would be unlikely to return before the World Cup break.
Postecoglou made six changes in all from the team that started the 3-1 loss to Leipzig with one eye on a second crack at the Germans on home soil on Tuesday.
Matt O’Riley’s deflected shot from 22 yards hit the outside of the post but St Johnstone held out until the 42nd minute when Sead Haksabanovic’s cross was turned into his own net by Andrew Considine at the near post.
Postecoglou’s men were guilty of passing up a number of chances to kill the game off and had two goals from Giakoumakis and Daizen Maeda ruled out for offside.
The visitors were given a warning when Joe Hart was forced to turn Stevie May’s shot onto the post.
Celtic were then punished for some very slack defending as Mitchell brought down Ali Crawford’s free-kick and stroked home from six yards.
But misfortune struck the Saints moments later as Drey Wright pulled up with cramp, allowing Bernabei to scamper clear down the left and his low cross was bundled in by Giakoumakis for his fourth goal of the season.
