Allardyce admitted Newcastle's players have proved themselves unable to tolerate the training techniques he believes are needed to ensure a successful season at St James's Park.
And, not for the first time, he blames the Glenn Roeder regime for allowing the first-team squad to become 'de-conditioned'.
Sam says it has left the club's players in no shape to deal with the demands that the modern game puts on top-flight footballers.
Although the Premier League season has not yet begun, United have 10 senior players on the injured list. It is a situation the Magpies manager believes is ridiculous.
Allardyce: "We're disappointed with the injuries we've got. It seems as though the players' tolerance levels are still very low. I warned everyone about that before I came. I felt that the players were de-conditioned to a point. It has been proven.
"We're trying to train in double shifts, that's what is needed at this stage in a pre-season campaign but the players haven't been able to tolerate it.
"We're having to work them in other areas and other ways with the sports science and medical staff to keep up their fitness while recovering from these niggles," he explained. "We're trying to give them three rehab sessions a day to (help them) get over their injuries and keep them as fit as we can."
Allardyce has conceded that his team will not be as fit as their opponents when Newcastle take on Bolton next weekend and that is a major annoyance.
The 52-year-old says he has yet to make the appointments that he hopes will enable him to replicate his Bolton back-room team at St James's Park. And when I looked at the over-flowing coaching bench at Hull on Wednesday I wondered what the hell half of them actually did for a living.
We had "Joker In The Pack" Terry McDermott looking none-plussed (as usual) making the substitutions. Can the man actually read? He had a piece of paper, a pen, and he looked bemused what to do with them.
Michael Owen and Shola Ameobi both seem certain to miss Newcastle's opening fixture at Bolton on August 11 having each played just 45 minutes under Allardyce this summer - the former with a thigh complaint, the latter with a back problem.
Albert Luque, Celestine Babayaro and David Rozehnal have all suffered groin strains in recent weeks. All are injuries that indicate that the players' base fitness levels are lacking.
Damien Duff was sidelined with an injured ankle that will rule him out until November prior to Allardyce's arrival, while Emre has not featured all summer and is receiving treatment on his ankle problem first suffered last season under a German specialist.
The Magpies boss has also suffered considerable ill-fortune. Having impressed on his debut following a £5.8m move from Manchester City, Joey Barton suffered a fractured metatarsal during his second appearance in Newcastle colours. Steven Taylor suffered a recurrence of an ankle injury during his first game under Allardyce's charge, while Nicky Butt's injured knee has ensured the former England international has played a limited role in recent weeks.
All 10 players missed this week's trip a Hull - a match in which Allardyce suffered his first defeat as United boss - and most will sit out this weekend's final pre-season fixture against Sampdoria.
Mark Viduka is expected to make his long-awaited debut, although with the campaign approaching fast, Allardyce's annoyance continues to mount.