After 15 games in the Premier League, West Ham find themselves 17th in the table, sitting one place above the relegation zone with just one win from their last eight games.
Allardyce acknowledged that the club's fortunes had not gone as expected this season, but reassured fans that they are doing everything to turn things around and hopes victory over rock-bottom Sunderland on Saturday will ease concerns.
And the 59-year-old revealed he is looking at strengthening his squad to give them a boost for the second half of the season.
"The supporters are frustrated," he said. "They didn't and we didn't expect to be where we are at this moment in time.
"When we played against Fulham we were in a similar position and alleviated some pressure but let ourselves down after that.
"The owners have always shown patience when dealing with a difficult situation, it's about picking up results and the pressure will go.
"What we want to try and look at all players that are available," he added. "Everyone knows that we're in the market for a player."
West Ham go into their match on Saturday knowing they have not beaten Sunderland in their last four meetings and have only scored once, while conceding eight.
