The Upton Park club are only above the relegation zone by virtue of their superior goal difference compared with Saturday's opponents Fulham, and have not picked up maximum points since their 3-0 win at Tottenham on October 6.
But Allardyce feels that his side's performances have merited more than they have yielded in recent weeks.
"Performances are okay for a while, but it's always about results," he said. "We haven't got the results so we have to try and get a massive victory (against Fulham).
"We haven't capitalised on our good play, scored the goals we needed to secure the three points in games.
"I'd have thought our victory at Spurs would have kicked us on, but it hasn't happened and we have to believe that we will start converting."
Allardyce has had to contend with an injury crisis among his strikers in the early months of the season, but he is hopeful that Andy Carroll will soon be ready to return from a foot problem that has kept him out for the whole of the campaign so far.
"We hope Andy will be back with us to start some training next week," the West Ham boss continued. "It's tentative in our approach to it.
"We can't get over anxious and push him too hard. We need to get him fit to stay fit."
