Rangers have won three games on the bounce and have kept three clean sheets but Beale has continued to remain an unpopular manager among the fans.
He has been taking criticism since their limp 1-0 win over Motherwell at Ibrox last weekend and many believe that he is one bad defeat away from getting sacked at Rangers.
Moore conceded that it is an unenviable position to be in for a manager when a large section of the fanbase have made up their mind about him and have turned against him.
The former Rangers star feels that he needs something in his favour soon as even if the team go on a good run, the fans will again criticise him after one poor result or performance.
Moore said on the Go Radio Football Show: “Michael is in a precarious position that he has the swell of the support against him.
“He needs to pull out something out of the bag for me.
“He can go on a run but that one poor performance or that one defeat, they are going to be on him again.”
Rangers fans are unlikely to tolerate it if their team lose to Livingston at Ibrox tonight in the Scottish League Cup quarter-final.