The Hoops crashed out of the Scottish Cup to bitter rivals Rangers.
Ronny Deila's men were beaten on penalties by Old Firm rivals Rangers at Hampden Park, but only after they had to equalise twice to even take the game that far.
But with the defeat meaning that their season now revolves around the league title, the defender has admitted that there is nothing that they can do to banish the painful memories from the dramatic semi-final.
"We've lost an Old Firm game and nothing really makes up for that," he told the Evening Times.
"It's done though, and we need to concentrate on the next thing now which is winning games for Celtic and winning the league."
Despite the Hoops playing in the division above, it appeared that it was Mark Warburton's men who were in the driving seat for much of the game. And Mulgrew has confirmed that the Bhoys did not do enough to win the game.
"We never played the way we could play and that's the most disappointing thing. To lose it on penalties is just a further blow," he added.
"There's no second chances, we didn't do it on the day and we can only blame ourselves."
With a comfortable lead over Aberdeen at the top of the table, Deila's men may well be in danger of dwelling on the defeat for longer as it is not essential that they get back to their best form any time soon. However, if the title race was much closer, they would have been forced to switch their attention back to the top flight almost as soon as the full-time whistle blew against the Gers.
But ultimately, Celtic may be unable to fully get over the defeat until they face their rivals in the league next season, regardless of whether they win a fifth league title in a row.