Allardyce has witnessed his side drop into the Premier League's bottom three after a run of seven league matches without a victory, with the club's last success coming in a 3-0 victory over Fulham at the end of November.
West Ham's situation has worsened with two drubbings in as many matches, the first a 5-0 thrashing at the hands of Championship out Nottingham Forest in the FA Cup, while Manchester City all but ended their hopes of reaching the League Cup final with a 6-0 win in Wednesday's semi-final first leg.
Co-chairmen David Gold and David Sullivan this week gave Allardyce a vote of confidence, but the 59-year-old concedes that his side must arrest their poor run of form soon, starting with Saturday's visit to Cardiff City.
When asked whether his position is under threat, Allardyce said: "You can't keep losing football matches as a manager, that's for sure.
"We know the reasons why, but even those reasons will not save you in the end.
"We must not lose confidence in our ability to get out of this hole we're in at the moment.
"We're going to start getting ready for Cardiff on Saturday and digging ourselves out of the bottom end of the Premier League."
West Ham's loss at City was met with anger by the club's supporters, who voiced their disapproval at the final whistle, and Allardyce says the reaction was understandable.
He added: "It's life. When you're not doing well, you're going to get stick. That's the way this job is. You have to take it on the chin and get on with it.
"You can understand it when they travel all this way and you get beat, you're going to get some criticism. It's life.
"But we're not the first team to get beat by many, many goals here and we won't be the last."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.