Postecoglou’s men hit the ground running as they looked to extend their lead at the top of the Scottish Premiership table and scored through Liel Abada with just 28 minutes on the clock.
They then doubled their advantage just three minutes later through Tom Rogic, who also scored again just before half time to make it 3-0 at the break.
Daizen Maeda grabbed a fourth for Celtic in the second half when a deflected effort of his looped into the back of the net and all three points were secured in style.
Former Motherwell man Craigan is hugely impressed with what he saw from Celtic at Fir Park and praised Postecoglou’s recruitment since he took over.
“You have to give Ange Postecoglou a big pat on the back, his recruitment has been outstanding”, Craigan said on BBC Sportsound.
“I think I counted nine out of the eleven players against Rangers were his signings.
“That is incredible.”
Postecoglou has revitalised Celtic since taking charge of the club in the summer, with the Bhoys turning to the Australian when Eddie Howe snubbed the chance to take over.
The former Australia boss has grabbed the opportunity with both hands and is now zeroing in on the title.