The £15m front man has not kicked a ball this season and West Ham have failed to score in four of their six league games.
Tomkins said: "Andy Carroll is a good player and his record speaks for itself, but we have a lot of ability in the side.
"We have good strikers and on their day they will play well against anyone, but we just have to sort out that aspect of our play as we are not scoring enough.
"We are maybe down on our luck a little because things aren't going for us but you have to earn your luck. We just have to keep working hard."
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