With club record signing Andy Carroll out injured, absent for the next couple of months at least, the Hammers have struggled in front of goal and failed to score in four of their six matches so far this season.
Sam Allardyce's men have not won since the opening day of the season against Cardiff and Tomkins believes that the players must take more responsibility for the team's lack of goals.
"Andy Carroll is a good player and his record speaks for itself, but we have a lot of ability in the side," Tomkins told the Daily Star.
"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."