Stephen Welsh and Carl Starfelt started in the centre of defence, both putting in excellent displays with the team recording their seventh clean sheet of the league campaign.
Since joining on loan from Tottenham Hotspur in the summer, Carter-Vickers has been an ever present for Ange Postecoglou.
The Australian revealed the reason he missed out.
"Just a personal issue so he misses out,” he told Sky Sports.
The 23-year-old has been impressive on the whole at the back for Celtic who have a clause in the deal which can allow them to make it permanent.
Postecoglou will hope he is back for Sunday’s clash with Dundee United after both Stephen Welsh and Anthony Ralston were replaced with injuries.
Nir Bitton finished the game at centre-back.