Postecoglou was irritated in particular with the first half performance of a much-changed side, even though they went in 1-0 up at half-time through Liam Scales' strike from outside the box. The home side's display in the second half was lifted by the introduction of some first team regulars off the bench and they eventually ran out comfortable winners as Giorgos Giakoumakis, Daizen Maeda and Nir Bitton struck in the final 22 minutes.
"We've got certain standards about how hard we want to work, what kind of football we want to play and how quickly we want to move the ball," Postecoglou told Premier Sports. "We were comfortable but I don't want us to be comfortable."
Celtic have already lifted the League Cup and lead the Scottish Premiership by a point in Postecoglou's first season in charge, but the former Australia boss rejected the idea that his squad are surpassing expectations. "We're nowhere near my expectations," he added. "As we saw in the first half today we've still got a lot of work to do."
Hibernian also booked their place in the quarter-finals after seeing off a potential upset at Championship leaders Arbroath to win 3-1. Craig Wighton fired the lower league side ahead after just six minutes.
Hibs had failed to win in their past five games to pile the pressure on manager Shaun Maloney early in his reign in charge. But they responded in terrible weather at Gayfield as Demetri Mitchell headed in a quick equaliser before second half goals from Kevin Nisbet and Chris Mueller secured a place in the last eight.