Rangers have already squandered their chance to be in the Champions League group stage and are four points behind Celtic in the league table following their Old Firm defeat at Ibrox on Sunday.
Michael Beale is under pressure and there are already worries about Celtic growing a large lead in the Scottish Premiership early on.
Ferguson insisted that in the situation the Scottish League Cup has become a must-win trophy for the Glasgow giants this season.
The Rangers legend stressed that he is not taking Livingston in the quarter-finals lightly, but insisted that the Rangers fans will demand that their side win the trophy by the end of the year.
Asked if Rangers have to win the Scottish League Cup, the former Gers captain said on the Go Radio Football Show: “I said two weeks ago, it’s a must, there is no doubt in my mind.
“I am not being disrespectful to Livingston who they drew in the quarter-final, Rangers have to deliver the League Cup in December.
“The fans will demand that.
“They are unhappy and they have got every right, they pay good money and they want to see [more].”
Rangers will take on Livingston in the quarter-final of the Scottish League Cup at Ibrox towards the end of the month.