Rogic was Celtic's only true spark against a determined Dundee defensive performance, but ultimately his side's failures in front of goal cost them.
The Australian was on the attack from the opening minute swinging in a dangerous cross which was hastily cleared.
Two great chances early in the second half should have seen Rogic with an assist and even a goal, but once again poor finishing cost Celtic.
Unimpressed by proceedings Rogers made a triple substitution in the 66th minute, removing big guns Rogic, Moussa Dembele and Scott Sinclair, but it was to no avail.
The point did move the treble-chasing home side 10 points clear of second-placed Aberdeen though, with six games remaining.
Andrew Nabbout recieved his first start at J-League club Urawa Red Diamonds overnight.
The Socceroos forward played the full 90 minutes but received a yellow card in the dying stages of their 0-0 draw with Sanfrecce Hiroshima.
Also in the J-League, former Socceroos coach Ange Postecoglou led his Yokohama F. Marinos team to a 3-1 win away to Albirex Niigata.
Australian defender Milos Degenek was an unused substitue in the clash.
And in England's League Two, Harry Kewell's Crawley Town played out a 1-1 draw with Swindon Town.
