Allardyce was unveiled as the Hammers' new manager on Wednesday after succeeding Avram Grant following their relegation to the npower Championship.
Hammer time: Sam Allardyce was officially unveiled as manager of West Ham on Wednesday
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.'
Speculation over the future of the club's high earners continues to rumble on following relegation, but Allardyce revealed the likes of England internationals Robert Green, Carlton Cole and Scott Parker have not been the subject of any formal bids.
'The speculation is around Rob Green, Carlton Cole and Scott Parker, and at the moment we haven't had any concrete bids for those players,' he said. 'Other than that there is no rush to sell anyone else.
Up for it: Allardyce relishing challenge of leading West Ham back into the Premier League before the club move to Olympic Stadium
'We will probably look at moving some of the players on because their desire is to play in Premier League.
'From a financial point of view, it suits us to lose that financial commitment because the drastic loss in revenue [following relegation] is what we all have to face at West Ham; certainly the owners, who've got to really back up with their own money to help us try to get back in the Premier League.
'We will try and get as good a squad as we can. There's some very good players at the club. If we all want to work together and go in the right direction, we can give it our best shot and hopefully that will be enough next season.'
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.
All change: Scott Parker is expected to be one of the star names to leave Upton Park this summer following relegation
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.'
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Explore more:People: Carlton Cole, Sam Allardyce, Robert Green Places: United Kingdom, Olympic Stadium