The London club were consigned to a 4-1 hammering at Liverpool last weekend and have now lost four of their last five top-flight matches.
That dismal run has left them languishing perilously above the relegation zone, level with Fulham and Crystal Palace - who are 18th and 19th respectively - and five points clear of Saturday's opponents.
Bottom-of-the-table Sunderland have picked up just two points on their travels in the Premier League this season, though, and West Ham boss Allardyce is not playing down the importance of his side's encounter against Gus Poyet's team.
He said: "It's a critical game for both teams. Both teams need to win and listening to Gus' quotes that's their objective.
"Every team in the Premier League can be difficult to break down and most games are decided by a bit of luck or mistakes that you make.
"We need all the lads that are available to step up to the plate and try and repeat the Fulham performance and get the same result."
Allardyce will have to do without skipper Kevin Nolan, who starts a three-match ban following his red card at Anfield, but fellow midfielder Ravel Morrison returns from suspension.
Defender James Tomkins (hamstring) will undergo a fitness test ahead of the match, but Allardyce expects James Collins and Guy Demel to be available despite being unwell this week.
Stewart Downing (leg wound), Winston Reid (ankle), Andy Carroll (foot), Mladen Petric (calf), and Ricardo Vaz Te (shoulder) are definitely out.
Sunderland are rooted to the foot of the table with only eight points from 15 games, and Tottenham condemned them to a third defeat in their last four last weekend.
Poyet's honeymoon period at the Stadium of Light is over, and the Uruguayan is eager to secure Sunderland’s first away win of the season at Upton Park.
"We know what we are coming up against and how difficult it will be," he told the club's official website.
"We need to stand up and do the right things all the time, be very strong as a group as well as being brave on the ball and making things difficult for them.
"Then, you always have a chance to win. We need to start winning games and we’ve got another opportunity on Saturday."
Poyet will be hoping Carlos Cuellar (hip) is available for the trip to London, but goalkeeper Keiren Westwood (shoulder) remains doubtful.
