The Hammers played out their fourth stalemate of the season on Saturday when they were held at home by Aston Villa.
Tomkins believes that West Ham just need to find the net once if they are to get their campaign up and running.
"Now we just need to get some wins in the bag," he told the club's official website.
"We've kept a lot of clean sheets and you need just one goal to change the game - we're looking for that one goal to set the season off."
Sunday's draw saw West Ham slip down to 15th place in the Premier League table.