Sam Allardyce's side are missing injured star striker Andy Carroll and have failed to find the net in four out of six top-flight games this term.
The latest blank came in the 1-0 defeat at Hull on Saturday, which left the Hammers in 17th place in the table, just a point above the drop zone.
Defender Tomkins has urged his team-mates to keep working hard to change their luck in front of goal.
He told the Daily Star: "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."
Among the misfiring strikers is Modibo Maiga, who has not found the net since December 2012, and West Ham boss Allardyce is looking for his goal drought to end.
He said: "He's struggling because he's not scored.
"He's paid to score a goal and when you buy a front man, he is up there to put balls in the net. Unfortunately, at this level, he's found that difficult to do.
"His contribution is all right in build-up terms but in the end it has to result in some form of goals."