The former Liverpool striker was unavailable his side's 2-0 opening-day win over Cardiff City on Saturday with a heel injury and, although the England international looks set to miss further games, the Hammers manager is confident that others can weigh in with goals, having seen Joe Cole and Kevin Nolan secure victory against the Welsh outfit at Upton Park.
"Sharing it about is what it's all about; we shared the goals out superbly well last year," Allardyce told reporters.
|16/1||West Ham are 16/1 with Bet365 to finish in the Premier League top six
"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 next Saturday but 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."