Carroll scored twice in last week's 3-1 defeat of West Brom which took the Hammers to 11th in the Barclays Premier League and virtually assured their safety.
The 24-year-old is on a season-long loan from Liverpool and unable to face his parent club just as he finds form which is sure to attract suitors this summer, although Allardyce is keen to keep the England striker.
"It's frustrating for him and for us, but that was the terms of the agreement," Allardyce said.
"He looks to be in full flow at the moment and in good goalscoring ability, which is what we've been waiting for for a long time.
"Our position in the league is strong again, so we want to continue that.
"We've got Carlton (Cole) and (Marouane) Chamakh who could step into the team and hopefully they can deliver the sort of performance Andy can deliver, because that's what we'll need at Anfield on Sunday."