Norwich currently sit inside the bottom three having accumulated eight points from their opening 10 league fixtures, with a 7-0 thrashing at Manchester City last weekend meaning the Canaries have taken just one point from the last 12 available.
But West Ham have also started slower than they did last season and defeat at Carrow Road would see them slip below Chris Hughton's Canaries, with Allardyce aware the fixture could be significant come the end of the season.
"It is a six-pointer already," he said.
"Norwich played very well in their last home game against Cardiff, I was listening to radio commentary and how many chances they created in that game and we have to make sure we do frustrate them in that area again on Saturday.
"If we can then take the game to them like we did in the 0-0 draw at Swansea this time we have got to make sure we are more clinical and put the ball in the back of the net."
Despite having only won twice so far this season, West Ham fans will remember their 3-0 success at rivals Tottenham for years to come.
But Allardyce is more concerned about taking points off the teams around them in the table rather than the occasional positive results against teams fighting at the top.
"It has always been more important for me," he said.
"Those are your games that if you play your best you have got a really good chance of winning. Whereas you can play your best against the big boys, give all you have got and be very, very good but still lose a game of football because of the amount of talent and the money they have spent.
"I always focus on these, they are the bigger games for us, the games you need to play at your best and give yourself a chance."
With Hughton's position as Norwich boss coming under scrutiny, especially from sections of the club's supporters, last weekend's hammering at the Etihad Stadium could leave the Canaries with problems on and off the pitch.
Allardyce, however, is taking the 7-0 result with a pinch of salt and believes Norwich will be looking for a positive reaction in Norfolk on Saturday evening.
"Manchester City are capable of beating anyone in their form at the moment," he added.
"We don't take anything from the Norwich defeat or the size of the defeat because, at the end of the day, I saw City tear apart a Champions League side [CSKA Moscow] in midweek.
"A loss is a loss, at the end of the day as a manager your mentality towards your players is still the same. It is still only three points that have gone, no more. You have lost 7-0 but you haven't lost five points, you'd have still lost only three points if you'd lost 1-0.
"We will get a Norwich City team that will come out and fight for everything they can. Particularly on their own ground and in front of a home crowd."