West Ham have endured a difficult campaign and have often flirted with relegation from the Premier League but, despite four straight defeats, are all but assured of their place in the top flight next season.
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Allardyce remains insistent he is the right man to improve the club's fortunes, though, and intends to remain in charge.
"I want to stay in my job and help take this club forward," he wrote in the London Evening Standard. "There is no point in treading water and just surviving.
"If that is the extent of your vision as a manager, then you have no ambition. I want to help grow this team so that they win more than they lose.
"There is no hiding the fact that we expected to do better this season. I saw the banner at West Brom last weekend and I understand the fans' frustrations.
"My first responsibility has to be to the people who employ me but I also have a commitment to the supporters of West Ham United.
"I don't take on the fans; there is no future in picking an argument with them. I understand their frustration, I really do. It's not what some of them say about me which really matters - it's that it can affect the players.
"If we're not doing as well as they would like - and we're not at the moment - their response can help turn that around, or it can make it worse.
"I know how difficult it is because they want to come to the Boleyn Ground, see their team do well and be excited by the football."