Allardyce said that the amount of money the big clubs can offer players means that the demands have gone up even for those without the ability to play for the top teams in England.
"The reality for us is this - we're not mathematically safe so we can't put any of our plans into practice," he told Sky Sports News. "We have the first draft, if you like, but we can't react on any of that at the moment. Our list in each position is accumulated and then you try and start to move forward on that list. It's a constant merry-go-round that we have to deal with in the difficult summer months.
"The great difficulty today is that you're competing with everybody else in a financial market that is sometimes unbalanced. The growth of wealth at the bigger clubs and what they can pay certainly has a cascading effect going down to the players that you want.
"If we all had the same amount of money to start the season with then it would make it a much more of an even playing field but it isn't like that now."
West Ham are currently 12th in the Premier League with 37 points.