The Hammers currently sit just one place above the relegation zone in the Premier League table on just goal difference having picked up 13 points from 15 games.
Allardyce believes that the pressure is on for the Hammers, but they are facing Gus Poyet's side, who are also in desperate need of points as Sunderland linger at the bottom of the standings.
"It's a critical game for both teams," Allardyce said in a press conference. "Both teams need to win and listening to Gus's quotes that's their objective."
West Ham have only won three times this season so far.