The Scottish Premiership leaders crashed out of the competition following a penalty shootout.
Chris Sutton has suggested that Celtic's Scottish Cup exit may be looked back upon as a blessing in disguise as it appears to have been the catalyst for Ronny Deila's decision to step down as Hoops boss, the Evening Times reports.
The Bhoys were beaten on penalties in the semi-final by their Old Firm rivals, and the defeat was followed a couple of days later by the news that the Norwegian is going to leave the club at the end of the season.
And Sutton believes that the news has provided something to be positive about in the wake of the Hampden Park defeat.
"Had Celtic won on Sunday and went on to win the double it would just have been papering over the cracks," he told the Evening Times.
"At least now people can see it. The failure to win big games had been going on for months, the fact they are one-dimensional. If he had stayed, Rangers' biggest asset next season would have been Ronny Deila. So Celtic needed to change. And the sooner they do it the better."
As the former Hoops forward suggests, winning the double may have potentially seen Deila stay on into next season, especially as they look set to win the Scottish Premiership comfortably and would have knocked their bitter rivals out on the way to Scottish Cup success.
But the style of play that the team has adopted has meant that many of their performances have been less than convincing. And in terms of the top flight, it is perhaps fair to say that Aberdeen's struggles have been as much a part of the Bhoys opening up an eight-point lead as their own form.
And with Rangers hinting that they could be capable of fighting somewhere near the top of the table next season, Celtic may not have been so lucky if they had played a similar way next season.