Boss Brendan Rodgers made seven changes to the team which started the 1-0 win over Zenit St Petersburg on Thursday evening (Friday morning AEDT) and they produced a disjointed performance in the first half.
The champions initially stepped up the pace after the break, but there was no onslaught and Saints held out for a welcome point.
Celtic finished the afternoon nine points ahead of Rangers and Aberdeen as they turn their attention to the second leg of their UEFA Europa League last-32 clash in Russia this week.
Hoops fans were boosted by the return of Rogic for the first time since he appeared in a UEFA Champions League clash against Anderlecht on December 5 after his recovery from a knee injury, with Cristian Gamboa, Jack Hendry, Calvin Miller, Charly Musonda, Odsonne Edouard and Scott Sinclair also back in.
In the absence of suspended skipper Scott Brown, Callum McGregor, who scored the winner against Zenit, was handed the armband.
Attacker George Williams, on loan from Fulham, was handed his Saints debut, with midfielder Blair Alston and striker Steven MacLean returning.
After the excitement of the Zenit game, Parkhead was much more subdued.
In the fifth minute a free-kick from winger Charly Musonda, on loan from Chelsea, was met by defender Kristoffer Ajer, but his header from point-blank range was parried by Saints goalkeeper Alan Mannus and the Perth defence scrambled the ball to safety.
Celtic keeper Dorus de Vries produced a moment of needless anxiety in the 14th minute when he mis-kicked straight to MacLean, but the striker could not take advantage as ball spun down from the air.
Saints came close just before the half-hour mark when David Weatherspoon's header from a Blair Alston cross flew just over the bar with De Vries beaten, before Saints fullback Richard Foster fired a drive from 25 yards over moments later.
Celtic had a good chance two minutes after the restart when Sinclair robbed Saints midfielder Chris Millar in the centre circle and raced forward before setting up Edouard.
However, the French striker hesitated inside the box and defender Jason Kerr blocked his shot which spun into the hands of a grateful Mannus.
Moments later, in a Saints break, Foster drove the ball across Celtic's six-yard box and past the far post before Mannus saved a long-range effort from Musonda at the expense of a corner which came to nothing.
The home supporters grew increasingly irritated and Rodgers introduced winger James Forrest for Rogic before Moussa Dembele came on for Edouard.
In between the two substitutions Mannus saved a Musonda free-kick and then Sinclair's follow-up drive, but still Celtic struggled to find any rhythm.
In the final, nervy stages Mannus saved down at his right from a Sinclair drive and Dembele headed wide before the final whistle allowed discontented fans to vent their frustration.