The Scotland international was forced off in the first-half after a nasty collision with Alloa midfielder Adam King, which left McGregor holding the side of his face in clear discomfort.
Downbeat Hoops manager Postecoglou feared his skipper would face an extended period on the sidelines in his post-match interview with a potential fractured cheekbone.
However, the Australian admitted he has since exchanged messages with McGregor and is hopeful he won’t be ruled out for too long.
Speaking exclusively to Celtic TV, Postecoglou said: “He’s better today, he wasn’t in great shape straight after the game.
“He probably had a slight concussion as well but I exchanged messages with him yesterday (Sunday) and he feels a bit better which is great.
“Hopefully his recovery doesn’t take too long.
“Knowing the type of character that Callum is, for him to stay down you knew it was something significant because he’s as brave as they come.
“He didn’t go all the way down and you could see he was trying to stay up. For him to come off, I knew it was something significant.”
Japanese midfielder Yosuke Ideguchi was also on the receiving end of a sickening challenge from Mouhamed Niang during the 2-1 victory and Postecoglou provided the latest on his condition.
He stated: “He’s not great. I said after the game it didn’t look too serious but to be fair I didn’t really get a good look at him.
“As everyone saw from the footage, it was a terrible tackle that should never have happened and it should’ve been addressed by the referee on the day.
“He hasn’t come out of it too well and he’ll be missing for a little bit as well. It was pretty painful, he tried to jog it off and I was optimistic it wasn’t anything too bad.”
Despite injuries to two players, Postecoglou was full of praise for goal scorer Giorgos Giakoumakis who has endured a rough start to life at Parkhead.
The Greek striker has been plagued by injury setbacks since his summer arrival from Dutch side VVV-Venlo.
Postecoglou added: “It was good for him to score and to get 90 minutes. He’s obviously had an interrupted first half of the season but he’s worked awfully hard during the winter break.
“We gave most of the players a week off but he stayed here at Lennoxtown with a few other boys and put in some additional work.
“He got through the 90 minutes pretty strong, so it’s a good foundation for him to build on.”
Postecoglou has enjoyed a productive January in the transfer market but he insists the club’s business might not be over yet.
With injuries and players heading off on international duty, Postecoglou could look to act before the end of the window, but he revealed the club are prioritising loan moves for several fringe players in the coming days.
He said: “We will stay alert and stay agile, there still could be some things that happen.
“We’re still looking at loans for a couple of our younger players, so I’m sure there’ll still be some activity between now and the end.
“What sort of activity that is, we’ll just see how it all develops.
“From our perspective, our planning has gone to schedule so far and hopefully that continues until the end of the window.”