Mulgrew made his return to Ronny Deila's side during the Scottish Cup victory over East Kilbride on Sunday.
Gary Mackay-Steven admitted that he was delighted to see both Charlie Mulgrew and Scott Brown back in the Celtic side after their spells on the sidelines, and believes that the pair will be crucial to the Hoops' chances of bagging silverware this season, the Evening Times reports.
The Scottish Cup victory over East Kilbride saw Mulgrew make his long-awaited return from a thigh injury, which had previously restricted him to one appearance in around five months (via Daily Record), while Brown made his third appearance since recovering from a knee injury that he sustained in November (via Daily Record).
And Mackay-Steven believes that the pair will have a huge influence on the side's form in the coming weeks.
"He [Mulgrew] is such a big player for us and is always in amongst it in the dressing room," he told the Evening Times. "But his versatility can be so important, as can the experience he has.
"We have him coming back and Scott [Brown] has also come back and they are two players who can be really vital for us in the run-in. They know what it takes to be successful at this club and they can hopefully help us because over the next few weeks they will get sharper and stronger as they get more minutes under their belts."
Their returns have undoubtedly come at the perfect time for Deila. The victory over the Lowland League side ended a poor week for the Bhoys on a positive note, but, given the stature of the opposition that was standing between Celtic and a quarter-final spot, the win would have done very little to relieve any of the pressure on the Norwegian.
While the Hoops were on cup duty, they had to look on as Aberdeen's victory over St Johnstone on Saturday meant that in the space of four days, the Dons had quashed a six-point deficit at the top of the Scottish Premiership table.
And while Deila's men have a game in hand over Derek McInnes' side, the loss to their nearest rivals in midweek, as well as the defeat to Ross County in the League Cup semi-final, has surely made it imperative that Mulgrew and Brown now remain fit, so they can use all of their experience to see the club through this difficult spell.