Carroll joined West Ham on a season-long loan from Liverpool before the transfer window closed and enjoyed an impressive debut in the 3-0 win over Fulham. However, the England international was forced off in the second half after hurting his hamstring and Hammers boss Allardyce is taking a cautious approach with Carroll's recovery.
"The next window of international break comes on October 6, so if he's fit before then we'll have done a magnificent job, but I probably don't think so," Allardyce told Goals on Sunday.
"I think it will be after that. "If the lads do the job they've started to do then it won't be too desperate to rush him straight back. "He's not had a lot of pre-season because of the European Championships and he didn't have a lot of football at Liverpool. "We've got to be very careful that we don't rush it too much and the hamstring might reoccur because that would be a disaster for us and for him."
Allardyce hopes the arrival of Carroll can help inspire Carlton Cole, who had an early shot cleared off the line during West Ham's 0-0 draw at Norwich.
"Carlton has got stiff competition because all of a sudden he has seen a centre-forward that has come from Liverpool, who Kenny [Dalglish] paid £35million for," said Allardyce. "It is one where you have to look at it and say 'what am I going to do? Am I going to shrivel up and die or am I going to roll up my sleeves and flight?' "In this league when you have got competition it has got to bring the best out of you, it is a simple as that."