Ange Postecoglou's first taste of an Old Firm derby has ended in defeat for his Celtic side, losing 1-0 to Rangers at Ibrox Stadium.

Scottish champions Rangers stretched their unbeaten Old Firm run to seven games after a second-half goal by Swedish defender Filip Helander.

The result left Rangers, who had won five of their previous six meetings against Celtic, third in the Scottish Premiership on nine points from four games after Helander headed home a Borna Barisic corner at the far post in the 67th minute.

Celtic stayed sixth on six points after suffering their second league defeat of the season, having been beaten by Hearts 2-1 in their opening game.

Postecoglou, who has quickly become a fan favourite at Celtic Park after an impressive start to the season, was left to rue early missed chances from his team

The Australian manager was left aghast when Celtic striker Odsonne Edouard missed a close-range sitter in the 25th minute, somehow scuffing his shot wide with the goal gaping.

"It was disappointing," Postecoglou said.

"Tight game, typical sort of derby game with not a lot of chances and not a lot of open space.

"The first goal was going to be critical and unfortunately we had the opportunity to do that and we didn't take it, and they did.

"We had the opportunity to grab hold of the game and we didn't take it. So it's still disappointing and something we need to make sure that, especially in these big games, when the moment arrives we take it."

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Rangers dominated after the break and Helander sent a packed home crowd into raptures when he met Barisic's cross to steer it past former England goalkeeper Joe Hart, who got a touch but could not keep the ball out.

Home keeper Robbie McCrorie twice denied Japanese forward Kyogo Furukashi an equaliser, rushing out to block him a minute after Rangers took the lead and then producing a superb reflex save in the 85th minute.

The derby defeat is a blow for Celtic, and Postecoglou said he was looking forward to the transfer window closing on Wednesday morning (AEST).

"We're keen to get to the end of the window so we can settle the squad down and do some work with the players," he said.

"On the other side of the window we'll know what squad we have and what players are in the picture for us moving forward and we can build."

ABC/Reuters