The Hammers have picked up just 13 points from 15 games in the Premier League so far this season, leaving them one place above the relegation zone in the table.
"The supporters are frustrated," Allardyce said in a press conference. "They didn't and we didn't expect to be where we are at this moment in time.
"The owners have always shown patience when dealing with a difficult situation. It's about picking up results and the pressure will go."
West Ham will take on Sunderland at Upton Park on Saturday.