McAllister won the English equivalent with Liverpool in 2001, alongside current Rangers manager Steven Gerrard.
The pair have once again made a positive start to life at Ibrox by progressing to the Europa League group stages and leading their team above Celtic in the early stages of the league.
However, McAllister knows that silverware could take them to another plane.
"With the Betfred Cup, and certainly south of the border as well with the League Cup, it was maybe the furthest one down on the list of priorities for most managers," he said.
"But I played in a treble-winning season and winning the League Cup was massive for us progressing in the other ones.
"If you can go ahead and win a cup early in the season, it doesn't half lift the place."
Rangers will play Scottish Championship side Ayr United at home on Wednesday in the cup.