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Forest, which parted ways with Nuno Espirito Santo earlier this month, is yet to win under its new boss, having succumbed to a 3-0 defeat away at Arsenal last Saturday. 

The Tricky Trees took a two-goal lead in the first half against the Championship side through an Igor Jesus double, but Alan Sheehan's team mounted a dramatic second-half comeback to stun the visitor. 

Having pulled one back in the 68th minute, Swansea captain Cameron Burgess netted the winner deep in stoppage time after Zan Vipotnik had restored parity.

Before the loss, Forest had advanced in 13 of its previous 15 Carabao Cup matches against lower-division opposition, winning its last four in succession since a 2-3 defeat to Burton Albion in the 2018-2019 fourth round.

A frustrated Postecoglou, who previously bullishly claimed he would have his new team fully up to speed with his methods in a matter of days, did not hide his frustration.

"I just thought it was a game we really should have killed off long before it got to the stage that it did," Postecoglou said. "I got the sense we were getting a bit comfortable and thought the game would finish off easily but that's not what happens, particularly in cup football. 

Postecoglou's team had the ball in the Swansea net a third time, just after the hour mark, but it was ruled out for offside. "I thought we scored a good third goal," Postecoglou said. "I think the lads got a bit comfortable in that moment and you've got to know the warning signs.

"We had to finish them off and we had plenty of opportunities to do that, and a couple of decisions didn't go our way.

"Players just thought it would naturally finish that way and we've paid a heavy price for that. We need to improve."

Forest next visits Burnley in the Premier League on Sunday.