The on-loan West Ham striker suffered a second serious problem of the season after damaging ligaments during the Hammers' 1-0 defeat against Manchester United in midweek
The striker is currently on a season-long loan from Liverpool but has struggled for fitness at Upton Park, missing several weeks earlier in the season with a hamstring problem.
Carroll, who netted his first goal of the season in last weekend's defeat to Tottenham, was substituted at Old Trafford not long after the hour mark and after further assessment from medical staff the England international has been ruled out for the remainder of the year.
"It is pretty severe - lateral ligament, I think," Allardyce told Sky Sports on Saturday.
"We did not expect it to be quite as severe as it was but it looks like maybe six to eight weeks. So that is a bit of a blow for us and Andy.
"But we must soldier on. There is not a lot we can do about these trauma injuries."
West Ham came from behind to beat Chelsea 3-1 without Carroll in Saturday's lunchtime kick-off after Carlton Cole, Mohamed Diame and Modibo Maiga scored to cancel out Juan Mata's opening goal.