Allardyce has always placed a major emphasis on high fitness levels at his previous clubs, particularly during his successful spell at Bolton, but he has not been impressed since taking over at Upton Park.
"Fitness has always been a massive part of football but never more so than now," he told Skysports.com. "If you haven't got the capabilities of an athlete, you can't be a top footballer.
"I've looked at their stats and it doesn't reflect well physically. It wasn't great. I was shocked considering the size of the squad and the quality of the players, many of whom were internationals. They really should have been pulling out much more.
"You look at their ability to perform at a high intensity and their sprint distances which is the level of speed needed to create the opportunities to win football matches.
"Compared to the levels at Blackburn and Bolton, they weren't good."