The Hammers slipped to a 1-0 defeat against fellow promoted side Reading on Saturday and have now won just one of their last eight Barclays Premier League fixtures.
Norwich, who had previously been on a 10-match unbeaten run, have lost their last three and Allardyce is hoping his players can end the congested festive period on a high.
"We need to bounce back," he said.
"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."
Allardyce has had to deal with a host of injuries in the past couple of months with key players such as Andy Carroll and Mohamed Diame still sidelined.
The 58-year-old believes the number of players unavailable to him of late has led to a slip in form that leaves the Hammers six points clear of the bottom three.
He said: "We haven't had our best team out for ages and since we beat Chelsea, our points total has diminished rather than kicked on from there.
"Normally when you get a result as big as that one you kick on and get more and more results as the euphoria keeps you going.
"The injuries have unfortunately kicked in and we've not been able to pick up the results we wanted to.
"It's about getting the players back fit and then keeping them fit, and then we'll be OK but that's got to happen very quickly now."
The recently recovered trio of Ricardo Vaz Te, Jack Collison and Alou Diarra were all in the matchday squad for the defeat at Reading with only the latter not making it onto the pitch at some stage.
But, despite welcoming a few players back from injury, Allardyce must now cope without the suspended duo of captain Kevin Nolan and defender James Collins for the match with Norwich.
"Losing the game (at Reading) was hard enough, but to lose two key players in the last game of the suspension period makes it even worse," he said.
"If they had got booked on Tuesday, there's no suspension, but they go and get booked at Reading and now we have to make do without them."
Collins was at fault for the goal at the Madejski Stadium on Saturday as his under-hit backpass was collected by Royals' striker Pavel Pogrebnyak, who then converted coolly past Jussi Jaaskelainen and the Wales international must now wait to make amends.
"James has to get over the mistake," said Allardyce.
"But unfortunately he can't on Tuesday as he's suspended. The rest of the team have to get over it and start getting a few more points."
With the Hammers on a run of poor form Allardyce is expecting a tense atmosphere at Upton Park for the visit of the Canaries.
"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."
Allardyce said he was not surprised to see Norwich string together an impressive run of form once their manager Chris Hughton became comfortable in his new surroundings at Carrow Road.
"They did so well last year, there was a little disruption with a change of manager that the club didn't expect," he said.
"A new manager gets his feet under the table and doesn't quite know his players and the players don't know him and once they get to do that and he gets to show he is a good manager and can replace Paul Lambert they start playing for him the way they are.
"It is no mean feat to go 10 games in the Premier League without defeat, that is a great, great run any of the top six sides would be pleased with that one never mind someone that is just competing in the Premier League for the second season running."