First-half strikes from midfielders Tom Rogic and James Forrest had the Northern Irishman's first piece of silverware since taking over the club in the summer all but guaranteed by the interval.
Striker Moussa Dembele confirmed that achievement when he scored from the penalty spot in the 63rd minute after Forrest was felled by Anthony O'Connor inside the box as the Scottish champions ran out convincing winners.
The former Swansea and Liverpool boss then played down the prospect of a domestic treble, saying: "I am thinking about Motherwell", Celtic's opponents next week.
Even so he had nothing but praise for his players and is targeting many more trophies in the years to come, after guiding Celtic to their 100th piece of silverware against the Dons.
"It is a winning club," he said. "That is what the great history of this club is based upon. It makes the milestone, that century of trophies over the course of history.
"And now we have to look to the next one and start the next century of trophies and that will be important for the club
"But for now it is a great night for the Celtic supporters to celebrate, they must have enjoyed the performance and, as I say, we push for the next one."