Guy Demel suffered concussion and James Tomkins was sent off in the much-needed 2-0 victory at fellow Premier League strugglers Cardiff City on Saturday.
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West Ham host Newcastle United in the top flight on Saturday and Rat has called on the players who are available to pull together, just as they did at Cardiff.
He told the club's official website: "It's like a curse! Every game we seem to get another injury, I don't know what we can do. The players that are fit have to be strong and try to get good results.
"We have not had much luck, so let's hope that it is starting to come back to us after Saturday.
"It's a good thing for us that Andy Carroll is back. He will give us a boost as he is the main man up front.
"He will get fitter and better with every game he plays."
Allardyce's charges moved out of the bottom three with their win last weekend, but full-back Rat is not paying too much attention to the table.
"I don't think about the bottom three, I just think to have back-to-back wins, just to play well and get a good result against Newcastle. That's the main thing," he added.