The Hammers were beaten by relegation-battlers Reading on Saturday and have now won just one of their last eight Premier League fixtures.
And Allardyce admits his side have lacked quality in recent matches, after finding the net just three times in their last four league fixtures since defeating Chelsea 3-1 in early December.
“We need to bounce back,” Allardyce told ITV Sport.
“We’ve got to make sure we become better at creating and taking our chances, otherwise it’s going to be tough.
“The balls into the box haven’t been given enough quality to open up a defence as everybody starts tightening up at this stage of the season.”
West Ham will look to return to winning ways in front of their home supporters against a Norwich side who have lost their last three matches since an impressive 10-match unbeaten run.
Despite the Norfolk-club’s recent form, Allardyce is wary of the threat posed by Canaries counter-attacks, and is expecting a tense atmosphere at Upton Park.
“I think it is going to be a big test for our nerve for the first time this season,” he said.
“Norwich have been very good defensively, particularly away from home and I think that they make life very difficult for you to break them down and play very well on the counter-attack if you leave too many spaces.”