The London club sit 19th in the Premier League and suffered an embarrassing 5-0 defeat at the hands of Championship outfit Nottingham Forest in the third round of the FA Cup on Sunday.
In an open letter posted on West Ham's official website, David Sullivan and David Gold acknowledged the "seriousness of our current predicament" but urged supporters to stick behind Allardyce and his team.
"We know Sam has not lost his ambition or desire and is committed to making West Ham United a great Premier League Club," read the letter.
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