The Hoops boss had hoped his midfielder would have been allowed to play against Rangers at Ibrox on December 29.
However, the Football Federation of Australia wants the entire squad to meet up in Dubai on December 27, the day after the Ladbrokes Premiership leaders play Aberdeen at Pittodrie, to prepare for the Asian Cup. Australia play their first game of the competition against Jordan on January 6.
After the 3-0 home win over Dundee at Parkhead, where 19-year-old Mikey Johnston scored twice before Filip Benkovic added a third, Rodgers said: “Tom will play in the Aberdeen game and he will fly out after that.
“He will miss the Rangers game as far as I am aware. It is a shame for him, a shame for us.
“We feel a sensible compromise could have been taken for all the players within their squad,, because you can’t say it is the same for everyone, because everyone is different, playing at different clubs and different levels.
“But if he is not involved, it is a shame, but we will just have to prepare without him.”
Johnston, standing in for the injured Odsonne Edouard, the Hoops’ only recognised centre forward, scored with a drive in the 42nd minute and a header just after the break.
Defender Benkovic added a third in the 69th minute to stretch the Hoops’ lead at the top of the table to three points over Aberdeen.
Rodgers said: “It was probably one of the most enjoyable games I have been involved in during my two-and-a-half years here.
“Sometimes the team at this part of the year has been a little bit leggy, but I really enjoyed watching us today.
“Even though it has been a struggle at times for Dundee this season, they have shown that they have some good players that can give you a problem.
“But we really stopped them playing and and the only downside was we only got three goals. It was really pleasing.”
The Northern Irishman was pleased with the performances of Johnston and right-back Anthony Ralston, both of whom have come through the Hoops academy.
He said: “I am aware that Mikey has played in the attacking positions across the front line and he has the instinct to score a goal.
“It was a brilliant piece of skill to score the way he did and the second one was the big surprise for us, he gets on the cross with a header and he was probably disappointed that he didn’t get a hat-trick today. I thought Tony Ralston was very good.”
Dundee boss Jim McIntyre had no complaints about the result.
He said: “Obviously it was a deserved scoreline. Celtic were very good, so fluid and caused us lots of problems.
“I thought our organisation, defending deep in the first half, was very good for about 30 minutes, but your concentration levels are so important when are playing that counter-attack style.
“The second half Celtic were just too good for us. Simple as that. We couldn’t cope with their movement, their interchanging and obviously we lost other goals.”