Celtic wingerJota has been ruled out of the League Cup final with a hamstring injury.
He was substituted during Celtic's 1-0 win over Hearts and with immediate fears he would be sidelined for several weeks.
Ahead of their final Europa League group match against Real Betis on Thursday, Postecoglou revealed the on-loan attacker is out for the showpiece occasion at Hampden Park on December 19.
"He won't be right for the cup final," the Australian said.
"It's going to be three-four weeks recovery depending how he goes so if you look at timelines it gets pretty tight for between now and the break."
Celtic are expected to trigger Jota's £6.5m option-to-buy clause before the end of the season.
The winger has impressed since moving from Portuguese club Benfica in the summer, scoring eight goals in all competitions so far.
A fee of £6.5m was agreed in the summer with Celtic eager to take advantage.
Sky Sports News understands Celtic are targeting moves for Japanese trio Daizen Maeda, Reo Hatate and Yosuke Ideguchi.
Manager Ange Postecoglou has already tapped into the J-League market with success, bringing in striker Kyogo Furuhashi from Vissel Kobe in the summer.
He would not confirm names but said things are progressing well for January.
"We are working hard on it, there are always things that you need to sort of overcome on a daily basis, particularly with the way the world is at the moment in terms of how we have discussions and how we follow up on things.
"I am still really happy with the way things are tracking and I still expect us to be well organised and have the people we want in place hopefully early in the transfer window.
There is nothing that has happened that has made me think that maybe we are not on schedule."
Celtic face eight games before the winter break starting with tomorrow night's Europa League showdown with Real Betis.
They have already secured third in Group G and will play in the conference League after Christmas, and that means Postecoglou will look to fringe players against Manuel Pellegrini's side.
"It makes sense for us tomorrow night to give some people a bit of a rest and also give some others some game time because we are definitely going to need them," he said.
"We saw that at the weekend, we had guys like Greg Taylor come back into the team, Mikey Johnson and it is really important that whenever we need to make changes that somehow we give players some game time and tomorrow night is a great opportunity to do that.
Defender Stephen Welsh returns to the squad for the game at Parkhead but the manager said he will be risk James Forrest or Anthony Ralston.