Leeds' new manager may have enjoyed hero status at Elland Road in his playing days but that will count for nothing unless he can whip into shape the squad he inherited from Dennis Wise.True, there were three new signings in the team that lost meekly to Tranmere, as well as defender Darren Kenton, whose loan spell had been turned into a permanent transfer.
Yet those players were targeted long before McAllister took charge and he had no time to exert much influence on yesterday's abject performance.
United, whose place in the top six has now been forfeited to Tranmere, have taken just one point from the last 12 available to them and alarmingly they have failed to score in three of their last four outings.
Work on the training field starts in earnest tomorrow as McAllister looks to weave his magic in time for the visit to Northampton at the weekend.
The new manager revealed that he will be paying close attention to improving leading scorer Jermaine Beckford's play.
Tranmere held Beckford in an iron grip and other teams have also made him a marked man. Although he has an impressive 16 goals so far this season, he has scored only once since the turn of the year.
McAllister said: "Jermaine is a young man and hopefully I can add a bit to his game. When a match is a bit scrappy like this one he can still play a part, rather than drifting."
Beckford was not the only Leeds player below par by a long chalk as Tranmere stretched their winning sequence to four matches.
Rovers manager Ronnie Moore argued that Saturday was probably the right time to be playing Leeds, before McAllister could exert his influence on the team, but you would have expected the players to bust a gut to impress their new boss.
Instead, McAllister was left to spell out to his new charges the importance of commitment and winning individual battles.
"I am aware of what it takes to get out of this league, you have to be competitive," said the new boss, who is renowned for his belief in attractive football.
"It is about getting results and there wasn't a lot of quality football here. There is a bit to do on the training ground to get us back on track. We have 16 games left to get out of this division and I know how many wins we need."
McAllister was without the injured Casper Ankergren and Frazer Richardson, while Tresor Kandol was missing with a sickness bug, but the manager conceded: "We had a strong 11 but never really got going."
Jennison Myrie-Williams opened the Leeds defence far too easily before beating keeper David Lucas with an angled shot in the 61st minute. Ian Moore, released by Wise in the summer, headed the second goal on his debut nine minutes later.
Moore, son of Rovers manager Ronnie, was all set to join Oldham on transfer deadline day before Tranmere hijacked his move from Hartlepool.
"I think that was my first headed goal of the season and it took me into double figures, but the three points were the most important thing," said Moore.
"At first it was in my head not to celebrate because I had some good times at Leeds but then I decided to run over to the Tranmere fans."
Moore added: "We stopped Jermaine Beckford from playing. If you do that you quieten Leeds.
"I was 15 minutes away from signing for Oldham before getting the text to go to Tranmere. Oldham were not pleased at all but I just wanted to go back to Tranmere because I had a great time there when I was 18 or 19."
The nearest Leeds came to scoring was when David Prutton took a free-kick from the left and saw it graze the bar just before half-time.