Allardyce was on Wednesday unveiled as the Hammers' new manager after succeeding Avram Grant following their relegation to the npower Championship.
And the former Bolton and Blackburn boss acknowledged promotion is all the more crucial with the club eventually set to move into the Olympic Stadium after next year's Games.
"I want to achieve the ultimate, which is to get promotion back to the Premier League at the first time of asking," Allardyce said. "As difficult as that is going to be, it can be achieved, I think.
"And with a club the size of West Ham that needs to be done as soon as possible.
"The long-term goal is the Olympic Stadium and the team must be back in the Premier League when it is going to move into that great venue."
Allardyce has yet to speak to any senior players at the club and admitted there was still much to be done.
"Before we all get together I've got an awful lot to sort out in terms of pre-season training, staffing, relocation for myself, so I'm going to try and do that before the players get back and then speak to them on an individual and group basis," he said.
Allardyce also bristled at the suggestion that he needed to win over the Hammers fans by playing attractive football - the so-called 'West Ham way'.
"When did West Ham play the West Ham way?" he said.
"It can't be the West Ham way if you get relegated, and the club's been up and down like a yo-yo [in recent years].
"I don't think the fans see that as playing the West Ham way.
"The West Ham way is about winning football matches and the enjoyment of winning.
"The fans are in the game to watch winning football, I'm in the game to play winning football and entertain the public, and that's what I do.
"Everywhere I've been I entertain the public, irrespective of the perception from the media that Sam Allardyce plays long ball.
"That is only a perception, but most of football is run on perception today."