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Giorgos Giakoumakis was the Hoops' hero, bundling home a close-range finish as the visitors grabbed all three points in a dramatic final act, leaving St Johnstone fans heartbroken just minutes after the elation of seeing Alex Mitchell net his leveller three minutes into stoppage-time.
But Postecoglou, who has become known for coining the term "never stop" as a slogan since moving to Scotland, wasn't completely happy with his side's performance, despite the win keeping it two points clear of fierce rival Rangers at the top of the Scottish Premier League.
“It’s a game we really should have put to bed a bit earlier with the chances [we had]," the former Australia coach said.
"At 1-0 they were always in the game, they threw a lot of balls into the box for a lot of big bodies and it doesn’t take much for them to get one over the line.
"It’s the fact that it happened so late on the game, it was going to be a real challenge for us, but we did it a few times last year and we’re going to have to do it this year if the game’s not going to run the way we want.
"We’re going to have to show that character and resilience to get over the line when we need to and credit to the boys, they did that.
"We’ve tried to instil that from day one, irrespective of the scoreline you go right to the end.
"We always score or we’re always a threat late in games irrespective of the score, so when you do need a late goal, we don’t have to change our approach, we just stick to what we do and I think that helps us.
"If we were a different type of team and all of a sudden we had to switch on to try to get a goal in some way, then it makes things more challenging."
