Although sidelined by only a slight groin strain, Given is concerned at having picked up another problem in an area which has troubled him for almost a year.
"I hope it's not psychological with Shay now, but it is bound to be," said Allardyce. "It's like Rooney getting three metatarsals.
"Shay has been as fit as a fiddle but in the last six months he has had a few injuries he has never had before. That is worrying him and worrying us. We want to eradicate that completely."
Allardyce added: "This injury is not in the same place specifically, but it's in the same areas and we need to strengthen all of those areas to dispel any fears he has that it might happen again, because that is what will cause it to happen again.
"Snatching at the ball, and pulling the leg round rather than stroking the ball like he normally does, can put huge pressure back on those areas. That is where the damage comes from."