The 25-year-old has endured a stop-start beginning to his Hammers career since arriving at Upton Park last summer after spending half of last season sidelined through injury.
Carroll will also miss the first four months of the 2014-15 campaign with a knee problem, but Allardyce, who spent a club-record £15m on him, says that he cannot be blamed for signing the towering forward.
"Everyone wanted to sign Andy Carroll when he finished the season [a year-long loan from Liverpool], everybody," he told reporters.
"There wasn't one person from the owners to any members of staff who didn't want to sign him.
"What we have to hope is eventually we will get him fit and he will produce a full season for us. We know what a big player he is for us."
West Ham open their 2014-15 Premier League season by hosting Tottenham Hotspur on Saturday afternoon.