Tottenham Hotspur must first navigate a Europa League fixture at Rangers this evening before making the trip to St Mary's on Sunday.
Postecoglou's side are 11th in the Premier League and he looks set to field 18 year old former Leeds United midfielder Archie Gray in central defence.
Spurs lost regular starters Cristian Romero and Micky van de Ven in their 4-3 defeat to Chelsea last time out, with both likely to need a spell in the treatment room.
Ben Davies is also sidelined with a hamstring injury, leaving Postecoglou with just one fit senior centre-half in Romanian international Radu Dragusin.
Former Saints star Fraser Forster, now 36, will also start in goal with Guglielmo Vicario sidelined after undergoing ankle surgery last month.
Ahead of trips to Glasgow and Southampton, Postecoglou said: "This is the worst I have experienced by a fair stretch but I never think it's just bad luck.
"Some of it is. I've never lost a goalkeeper for this period, but some of it is recurring, particularly this year in terms of guys coming back and re-injuring.
"It's something we're looking at and we're always trying to explore whether we can do things better. Last year was different, last year it hit us across the board.
"This year it's more guys that are coming back who are affected. Knock on wood, we've got a core group who are playing a lot and are getting through it ok.
"Archie's done right back, left back for us and had to play at centre-back a little bit this year. With him and Radu, they're the two main sort of defenders.
"We've still got five or six games to navigate so we may have to get creative at some point and deal with it in a different way."
Wilson Odobert, Richarlison, Mikey Moore and Yves Bissouma are also sidelined while midfielder Rodrigo Bentancur is still serving a seven-match suspension.
Under pressure Postecoglou added: "It’s challenging. It’s no secret we’re thin on numbers both squad-wise and position-wise but it is what is.
"We can’t change it. we’ve got some big games coming up, we’ll have to deal with what we’ve got. I’m confident we’ll be able to get the job done."
Saints will take on Spurs from 7pm on Sunday, knowing even a win will not be enough to climb off the bottom of the Premier League table.