Sam Allardyce's side have drawn blanks in four of their six Premier League fixtures this season, the latest of which came in Saturday's 1-0 loss away to Hull City, leaving the Hammers just outside the bottom three in 17th position.
|WEST HAM LATEST
|6/1||West Ham are 6/1 with BetVictor to be relegated
"Andy Carroll is a good player and his record speaks for itself, but we have a lot of ability in the side," he 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."
West Ham's loss to Hull came in controversial circumstances, with Robbie Brady going down under minimal contact to earn the game-winning penalty, but Tomkins refused to criticise referee Kevin Friend.
"The lad's gone down from Joey [O'Brien]'s challenge and he's bought the foul really. The referee has fallen for it and it's one of those things," the centre-back added on the club's official website.
"We can't blame the referee though, we've got to look at ourselves and work hard this week.
"From the penalty onwards on we looked the better team. We could have scored - we created a lot of chances - and we might have had a penalty ourselves, but the decisions have gone against us."