The former Liverpool striker missed his side's 2-0 win over Cardiff City on Saturday with a heel injury.
Although the England international looks set to miss further games, Allardyce is confident other squad members can weigh in with goals, having seen Joe Cole and Kevin Nolan secure victory against the Welsh side at Upton Park.
"Sharing it about is what it's all about, we shared the goals out superbly well last year," he said.
"Kevin got 10, Andy got eight and the rest of the lads got twos and ones and threes all over the park which was great in helping us get to 10th.
"(Modibo Maiga) has got some goals in him and we think the more he plays and the more opportunities he gets, the more he'll score.
"Kevin is a Premier League goalscorer if used in the right way.
"He's always scored a huge amount of goals which is very, very difficult today. There's only Frank Lampard who probably scores more than him from midfield."
Allardyce confirmed that Carroll will not feature against former club Newcastle United next Saturday and does not envisage any further additions to his squad because of financial restraints.
"He won't be fit (for the Newcastle game)," the 58-year-old added. "He hasn't joined in training with us yet which is obviously our major concern.
"I've no budget left, I've no money left. I can't see (signings) happening as we've no budget at the moment."
