The Hammers travel to face local rivals Tottenham on Wednesday for a place in the final four of the cup but sit 17th in the table, just one point clear of the relegation zone.
A drab 0-0 draw at home to bottom side Sunderland on Saturday would have been seen as a missed opportunity to move further clear of the bottom three and, with a trip to face reigning champions Manchester United on Saturday and a Boxing Day clash with league-leaders Arsenal, Allardyce will remain focused on those fixtures despite a trip to White Hart Lane.
"I have got to get a team ready to get some points at Manchester United," he said.
"That is not just my format that is everybody's format here including the owners. Premier League status is the most important thing for the club.
"The more important game for me, as much as I don't like to say it, is Manchester United and getting points unfortunately rather than Tottenham on Wednesday based on the position I am in the league and with the squad I have available at the moment.
"I would like to be in a much better position, I remember playing Cardiff here and playing the first-team behind the first-team.
"When we got round to Burnley that diminished somewhat with the injuries we had then so we played a lot of the young players.
"We have to see what we have available for Wednesday night and play the team that we can put out."
The highlight of West Ham's campaign so far undoubtedly came when they won 3-0 at Tottenham on October 6, but since then Allardyce's side have only taken six points from nine fixtures.
They have the most number of clean sheets in the division but, with record summer-signing Andy Carroll still yet to feature this season due to a heel problem, the Hammers have struggled to find the back of the net.
Only Cardiff and Sunderland have scored fewer than West Ham's 13 Premier League goals and Allardyce has admitted he is looking to add more attacking threat to his squad when the January transfer window opens.
The 59-year-old said in his programme notes ahead of the stalemate with Sunderland that the club were in negotiations to bring in at least one player and, when asked after the game, he confirmed it is an individual he hopes will make a difference at the top end of the pitch.
"It is an attacking player there are no doubts about that," he added.
"We are moving on to the next phase and we are talking to the club and the player's agent to see if he is going to join us or not.
"We will try and do the deal as quickly as we possibly can, [co-chairman] David Sullivan is the quickest owner of a football club I have ever had. He doesn't 'ooh' 'ahh' and 'um' like most of the other owners I have been involved with."
Sullivan said on Saturday that Allardyce would remain in charge until the end of the season but, with West Ham the only club in the current bottom five not to change their manager this season, the former Bolton and Newcastle boss will not be resting on his laurels.