The Hammers have dropped into the Premier League's bottom three after seven league games without a win, exited the FA Cup on Sunday after being hammered 5-0 by the Championship's Nottingham Forest and then were battered 6-0 by Manchester City in the first leg of their Capital One Cup semi-final on Wednesday.
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Asked by reporters whether his position is under threat, the Hammers boss replied: "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 that the reaction was understandable.
"It's life," he added. "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."