The Hammers have finished in 10th and 13th place in their previous two campaigns following their promotion back to the top flight in 2012.
Alladyce feels that his side need to make a mark this year as a team who are a permanent fixture in the Premier League.
He told reporters: "If you look at the numbers, most teams finish around where their budget is. We'll be around 10th, 11th, I think. That's somewhere we want to try and achieve.
"It's year three for us so we should be looking more to establish ourselves rather than worrying about relegation.
"In terms of what the chairmen and the fans expect – all of that's fine. We can all say that I want the same, but the reality is we know how to get there."
West Ham face Crystal Palace in their second Premier League clash later today.