England international Carroll is struggling with a heel injury and Allardyce's side have struggled in his absence, scoring just four goals in six Premier League games.
Next up for West Ham is a trip to Tottenham on Sunday and Allardyce is keen for them to make the most of the opportunities they are creating, after they spurned numerous chances to score in the 1-0 defeat by Hull last weekend.
"Our season doesn't hinge on Andy getting back. He is a big player in many ways, but our failing is not that we have lacked chances," he said.
"What we have lacked is taking them and our players can't keep missing them.
"We had 19 attempts on goal away from home in the Premier League last week. We dominated the game but failed to score.
"All the other players getting these chances have failed to put one in the net, and that's why we're suffering the consequences.
"We've always been a team who have shared the goals out, but we're not doing that at the moment."
Allardyce confirmed he will not risk starting Joe Cole against Spurs, although the midfielder may earn a place on the substitutes' bench.
"Joe Cole is not ready to start because we haven't seen him on the pitch for a while, but we hope he is ready to be in the squad," added Allardyce.
"He's back in full training but I think starting after such a long period out wouldn't be right.
"Getting him on the bench would be good from our point of view."