The Hammers slipped to a 1-0 loss against fellow promoted side Reading on Saturday and have now won just one of their last eight 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.
"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," said Allardyce.
"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."
He added: "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."