The Hammers head to Carrow Road looking to end a three-match winless run in the league which has seen them slip to 15th place in the table with 10 points.
They have also failed to find the net in their last two games - goalless draws with Swansea and Aston Villa - and Allardyce sees this as an ideal chance to end their barren streak in front of goal.
The Canaries are without a win in their last four league fixtures - a run which has seen them pick up only one point from a 0-0 home draw with Cardiff - and conceded seven goals in last weekend's thrashing at Manchester City.
Allardyce said: "Norwich is a six-pointer already. They played well in their last home game against Cardiff and we have to make sure we frustrate them in that area and be clinical when we get our chances.
"We've done alright so far in performance terms, but unfortunately because of our lack of goals we haven't accumulated the points.
"We've played some good football but the end product hasn't been there and that's why we've drawn games we should have won.
"There's nothing else to concern me other than not taking our opportunities but we've got to start doing that as soon as possible."
Allardyce revealed Winston Reid is a doubt for the trip to Norwich although fellow defender James Collins is now back in training.
He added: "It's not very good injury wise at the moment other than we've got James Collins back in training.
"Winston Reid picked up an unfortunate one this week which adds to the list."
Watch Norwich v West Ham live on Sky Sports 1HD from 5pm on Saturday.