The Hammers, who gained promotion from the Championship via the play-offs last term, currently sit in 11th place in the top flight.
But, with his side having lost three of their last four league fixtures, Allardyce is hoping for a run of good results to cement their mid-table status.
"If you can pick up a couple of wins back-to-back or get a few points in the bag you can climb the table,” he told the club’s official website.
“You saw recently with Stoke, who had not won away from home and had drawn a lot of their games, all of a sudden they strung two or three wins together and they are back at the top end of the Premier League.
“Sticking a few wins together is where you want to be over Christmas because it sends you into the New Year in a relatively comfortable position - particularly in our first year back in the Premier League.
“Hopefully we can overcome our injury crisis and can continue to pick up the results we've been getting this season."
Allardyce also revealed he will be looking to bring some new players to Upton Park during the January transfer window.
He added: “We will be trying to buy some players and those players will be determined on what we want to do and then we'll try to make the moves happen.
“Like anything else in that window, it's a hard window to deal with and it becomes very disruptive for everybody, but we've got to try to do our best to try to strengthen the squad where we can."
The former Bolton manager went on explain that he is wary of the threat posed by West Brom on Sunday, with the Baggies looking to arrest a run of three defeats on the bounce.
|25/1||West Ham are 25/1 to be relegated with Bet365|
“Only two very poor refereeing decisions cost them the game so they may well have got something against Arsenal.
“At this moment in time, they are still playing very well but results have not matched the performances they have given. Their home form has been very good this year.
“Three defeats on the trot may put a little bit of doubt in their players and if that's the case we have to try and exploit that.
“We have our own problems with injuries so we have to rely on the players we have available to give their best again like they did against Liverpool and I hope that will be enough to get us a result at West Brom.”