The Hammers have scored just eight times in 10 Premier League games this season and their 59-year-old manager is concerned about their inability to take their chances
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Allardyce has been without main striker Andy Carroll all season as he continues to recover from an Achilles injury, while backup forwards Modibo Maiga and Ricardo Vaz Te have struggled to find the back of the net.
The lack of goals has left West Ham in 15th in the table but Allardyce believes that their position does not reflect their displays.
"We've done alright so far in performance terms but unfortunately because of our lack of goals we haven't accumulated the points," he said ahead of West Ham's trip to Norwich on Saturday.
"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."
Carlton Cole has re-signed with the club after being released during the close-season to provide more options, though he has been restricted to just two substitute appearances in the league as he works towards full fitness.